<PAGE>   1
                                UNITED STATES
                     SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549
                                  FORM 10-Q

[x]   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
      EXCHANGE ACT OF 1934

      For the quarterly period ended June 30, 1998

                                     OR

[ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
      EXCHANGE ACT OF 1934.

      For the transition period from                 to

      COMMISSION FILE NUMBER  0-26466

                         TAPPAN ZEE FINANCIAL, INC.
           (Exact name of registrant as specified in its charter)

      DELAWARE                                            13-3840352
(State or other jurisdiction of                        (I.R.S. Employer
incorporation or organization)                       Identification Number)

75 NORTH BROADWAY, TARRYTOWN, NEW YORK                     10591-0187
(Address of principal executive offices)                   (Zip Code)

                               (914) 631-0344
            (Registrant's telephone number, including area code)


Indicate by check mark whether the registrant (1) has filed all the reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. YES X NO __

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

<TABLE>
<CAPTION>
      CLASSES OF COMMON STOCK       NUMBER OF SHARES OUTSTANDING, JUNE 30, 1998
      -----------------------       -------------------------------------------
<S>                                 <C>      
            $.01 Par Value                           1,478,062
</TABLE>
<PAGE>   2
                         TAPPAN ZEE FINANCIAL, INC.

                         PART I - FINANCIAL INFORMATION

<TABLE>
<CAPTION>
                                                                                Page
                                                                                ----
<S>                                                                             <C>
Item 1.  Financial Statements (Unaudited).

          Consolidated Balance Sheets at                                          2
           June 30, 1998 and March 31, 1998

          Consolidated Statements of Income for
           the Three Months Ended June 30, 1998 and 1997                          3

          Consolidated Statement of Changes in Shareholders'
           Equity for the Three Months Ended June 30, 1998                        4

          Consolidated Statements of Cash Flows
           for the Three Months Ended June 30, 1998 and 1997                      5

          Notes to Consolidated Financial Statements                              6

Item 2.  Management's Discussion and Analysis of Financial Condition and
          Results of Operations.                                                  9

Item 3.  Quantitative and Qualitative Disclosures About Market Risk.             18

                       PART II - OTHER INFORMATION

Item 1.  Legal Proceedings.                                                      19
Item 2.  Changes in Securities.                                                  19

Item 3.  Defaults Upon Senior Securities.                                        19

Item 4.  Submission of  Matters to a Vote of Security Holders.                   19

Item 5.  Other Information.                                                      19

Item 6.  Exhibits and Reports on Form 8-K.                                       19

Signature Page.                                                                  20
</TABLE>

Explanatory Note: This Quarterly Report on Form 10-Q contains certain
forward-looking statements consisting of estimates with respect to the financial
condition, results of operations and business of the Company that are subject to
various factors which could cause actual results to differ materially from these
estimates. These factors include changes in general, economic and market, and
legislative and regulatory conditions, and the development of an interest rate
environment that adversely affects the interest rate spread or other income
anticipated from the Company's operations and investments.


                                       1
<PAGE>   3
                   TAPPAN ZEE FINANCIAL, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                   (UNAUDITED)
                        (IN THOUSANDS, EXCEPT SHARE DATA)

<TABLE>
<CAPTION>
                                                                                             JUNE 30,         MARCH 31,
                                                                                               1998             1998
                                                                                            ---------        ---------

                                           ASSETS
<S>                                                                                         <C>              <C>      
Cash and due from banks                                                                     $     962        $     783
Interest-bearing deposits                                                                       1,295            2,401
Federal funds sold                                                                              5,500            6,200
                                                                                            ---------        ---------
     Cash and cash equivalents                                                                  7,757            9,384
Securities:
    Available-for-sale, at fair value (amortized cost of $27,488 at June 30, 1998 and
        $22,719 at March 31, 1998)                                                             27,676           22,868
    Held-to-maturity, at amortized cost (fair value of $43,494 at June 30, 1998 and
        $35,971 at March 31, 1998)                                                             43,053           35,531
                                                                                            ---------        ---------
        Total securities                                                                       70,729           58,399
Loans, net:
    Mortgage loans                                                                             54,351           54,915
    Other loans                                                                                 3,516            3,673
    Allowance for loan losses                                                                    (708)            (702)
    Net deferred loan fees                                                                       (257)            (263)
                                                                                            ---------        ---------
         Total loans, net                                                                      56,902           57,623
Federal Home Loan Bank stock                                                                      943              943
Other assets                                                                                    3,359            2,996
                                                                                            ---------        ---------
         Total assets                                                                       $ 139,690        $ 129,345
                                                                                            =========        =========

                            LIABILITIES AND SHAREHOLDERS' EQUITY
Liabilities:
    Deposits                                                                                $ 105,222        $ 104,993
    Federal Home Loan Bank advances                                                            10,000               --
    Other liabilities                                                                           2,333            2,552
                                                                                            ---------        ---------
         Total liabilities                                                                    117,555          107,545
                                                                                            ---------        ---------
Shareholders' equity:
     Preferred stock (par value $0.01 per share; 1,000,000
         shares authorized; none issued or outstanding)                                            --               --
     Common stock (par value $0.01 per share; 5,000,000
         shares authorized; 1,620,062 shares issued)                                               16               16
     Additional paid-in capital                                                                15,124           15,086
     Common stock held by employee stock ownership plan ("ESOP")                                 (867)            (904)
     Common stock awarded under recognition and retention plans ("RRPs")                         (370)            (401)
     Treasury stock, at cost (142,000 shares)                                                  (2,060)          (2,060)
     Retained earnings, substantially restricted                                               10,179            9,974
     Other comprehensive income                                                                   113               89
                                                                                            ---------        ---------
         Total shareholders' equity                                                            22,135           21,800
                                                                                            ---------        ---------

         Total liabilities and shareholders' equity                                         $ 139,690        $ 129,345
                                                                                            =========        =========
</TABLE>


See accompanying notes to unaudited consolidated financial statements.


                                       2
<PAGE>   4
                   TAPPAN ZEE FINANCIAL, INC. AND SUBSIDIARIES
                        CONSOLIDATED STATEMENTS OF INCOME
                                   (UNAUDITED)
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)

<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED JUNE 30,
                                                                ---------------------------
                                                                     1998         1997
                                                                   ------       ------
Interest income:
<S>                                                             <C>             <C>   
     Mortgage loans                                                $1,153       $1,098
     Other loans                                                       83          101
     Securities                                                     1,135          894
     Other earning assets                                             106          172
                                                                   ------       ------
         Total interest income                                      2,477        2,265
                                                                   ------       ------
Interest expense:
      Deposits                                                      1,212        1,132
      Federal Home Loan Bank advances                                  69           --
                                                                   ------       ------
         Total interest expense                                     1,281        1,132
                                                                   ------       ------

         Net interest income                                        1,196        1,133
Provision for loan losses                                              10           11
                                                                   ------       ------
         Net interest income after provision for loan losses        1,186        1,122
                                                                   ------       ------

Non-interest income:
     Service charges and other fees                                    35           34
     Net gain on sales of available-for-sale securities                --           11
     Other                                                              7            5
                                                                   ------       ------
         Total non-interest income                                     42           50
                                                                   ------       ------

Non-interest expense:
     Compensation and benefits                                        446          410
     Professional services                                             55           72
     Occupancy and equipment                                           43           46
     Data processing service fees                                      47           42
     Federal deposit insurance costs                                   17           15
     Other                                                            121          129
                                                                   ------       ------
         Total non-interest expense                                   729          714
                                                                   ------       ------

         Income before income tax expense                             499          458
Income tax expense                                                    197          193
                                                                   ------       ------
         Net income                                                $  302       $  265
                                                                   ======       ======

Basic earnings per share (note 3)                                  $ 0.22       $ 0.19
                                                                   ======       ======

Diluted earnings per share (note 3)                                $ 0.21       $ 0.19
                                                                   ======       ======
</TABLE>


See accompanying notes to unaudited consolidated financial statements.


                                       3
<PAGE>   5
                   TAPPAN ZEE FINANCIAL, INC. AND SUBSIDIARIES
           CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS' EQUITY
                                   (UNAUDITED)
                  (DOLLARS IN THOUSANDS, EXCEPT PER SHARE DATA)


<TABLE>
<CAPTION>
                                                         COMMON      COMMON                                OTHER
                                           ADDITIONAL     STOCK       STOCK                               COMPRE-        TOTAL
                                   COMMON   PAID-IN       HELD      AWARDED    TREASURY      RETAINED    HENSIVE    SHAREHOLDERS'
                                    STOCK   CAPITAL     BY ESOP     UNDER RRPS   STOCK       EARNINGS     INCOME        EQUITY
                                    -----   -------     -------     ----------   -----       --------     ------        ------
<S>                                 <C>     <C>         <C>         <C>         <C>          <C>          <C>        <C>     
Balance at March 31, 1998            $ 16    $ 15,086     $ (904)   $ (401)     $ (2,060)     $ 9,974        $ 89     $ 21,800

   Net income                          --          --         --        --            --          302          --          302
   Dividends paid ($0.07 per
     share)                            --          --         --        --            --          (97)         --          (97)
   Amortization of RRP awards          --          --         --        31            --           --          --           31
   ESOP shares committed to be
      released (3,674 shares)          --          38         37        --            --           --          --           75
   Increase in other
     comprehensive income              --          --         --        --            --           --          24           24
                                     ----    --------     ------    ------      --------     --------       -----     --------
Balance at June 30, 1998             $ 16    $ 15,124     $ (867)   $ (370)     $ (2,060)    $ 10,179       $ 113     $ 22,135
                                     ====    ========     ======    ======      ========     ========       =====     ========
</TABLE>


                                       4
<PAGE>   6
                   TAPPAN ZEE FINANCIAL, INC. AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                             THREE MONTHS ENDED JUNE 30,
                                                                                 1998            1997
                                                                              --------        --------
<S>                                                                           <C>             <C>     
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income                                                                  $    302        $    265
  Adjustments to reconcile net income to net cash provided
     by operating activities:
     Provision for loan losses                                                      10              11
     Depreciation expense                                                           13              14
     Accretion of net deferred loan fees                                           (16)             (8)
     Net increase in accrued interest receivable                                   (90)            (23)
     Net gain on sales of available-for-sale securities                             --             (11)
     Noncash ESOP and RRP expense                                                  106              94
     Other adjustments, net                                                       (356)            (73)
                                                                              --------        --------
          Net cash (used in) provided by operating activities                      (31)            269
                                                                              --------        --------

CASH FLOWS FROM INVESTING ACTIVITIES:
  Purchases of securities:
     Available-for-sale                                                         (7,926)         (2,000)
     Held-to-maturity                                                          (10,125)           (500)
  Proceeds from principal payments, maturities and calls of securities:
     Available-for-sale                                                          3,155           5,040
     Held-to-maturity                                                            2,605             397
  Proceeds from sales of available-for-sale securities                              --           2,511
  Disbursements for loan originations                                           (1,797)         (2,263)
  Principal collections on loans                                                 2,524           1,248
  Other investing cash flows, net                                                   (2)             --
                                                                              --------        --------
          Net cash ( used in) provided by  investing activities                (11,566)          4,433
                                                                              --------        --------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Net increase in deposits                                                         229           2,539
  Net increase in short-term borrowings                                         10,000              --
  Purchase of treasury stock                                                        --            (633)
  Dividends paid                                                                   (97)           (101)
  Net decrease in mortgage escrow funds                                           (162)           (151)
                                                                              --------        --------
          Net cash provided by financing activities                              9,970           1,654
                                                                              --------        --------

Net (decrease) increase in cash and cash equivalents                            (1,627)          6,356

Cash and cash equivalents at beginning of period                                 9,384           8,250
                                                                              --------        --------

Cash and cash equivalents at end of period                                    $  7,757        $ 14,606
                                                                              ========        ========

Supplemental information:
  Interest paid                                                               $  1,230        $  1,132
  Income taxes paid                                                                430             310
                                                                              ========        ========
</TABLE>

See accompanying notes to unaudited consolidated financial statements.


                                       5
<PAGE>   7
                   TAPPAN ZEE FINANCIAL, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)

(1)      Basis of Presentation

   Tappan Zee Financial, Inc. (the "Registrant") is the savings bank holding
company for Tarrytowns Bank, FSB (the "Bank"), a federally chartered savings
bank and wholly-owned subsidiary of the Registrant. On October 5, 1995, the Bank
converted from a mutual savings bank to a stock savings bank (the "Conversion").
Concurrent with the Conversion, the Registrant sold 1,620,062 shares of its
common stock in a subscription and community offering at a price of $10 per
share, for net proceeds of $14.9 million (the "Stock Offering"). In March 1998,
the Registrant established TPNZ Preferred Funding Corporation ("TZPFC"), as a
wholly-owned subsidiary. The purpose of TZPFC is to acquire and manage a
portfolio of mortgage loans and mortgage-backed securities. TZPFC is intended to
qualify as a real estate investment trust for tax purposes. Collectively, the
Registrant, TZPFC and the Bank are referred to herein as the "Company".

     On March 6, 1998, the Registrant entered into an Agreement and Plan of
Merger with U.S.B. Holding Co., Inc. ("USB") (the "Merger Agreement") pursuant
to which the Registrant will merge with and into USB, a registered bank holding
company and parent company of Union State Bank, a New York State chartered
commercial bank. The Bank will operate as a wholly-owned subsidiary of USB.

      Under the terms of the Merger Agreement, each shareholder of the
Registrant will receive USB common stock based on an exchange ratio which will
be determined based upon the average of the last reported sales prices for a
share of USB common stock for the 20 consecutive full trading days on the
American Stock Exchange ending on the date of receipt of the last regulatory
approvals (the "Average Closing Price"). The minimum exchange ratio will be 0.88
shares of USB common stock for each share of Registrant common stock, if the
Average Closing Price of USB's common stock has a value of $25.00 per share, or
higher, and subject to the exception below, the maximum exchange ratio will be
1.24 shares of USB common stock for each share of Registrant common stock if the
Average Closing Price of USB's common stock has a value of $17.75, or lower. If
the Average Closing Price of USB's common stock is between $17.75 and $25.00 per
share, the Exchange Ratio will be established to provide a value to the
Registrant's shareholders of $22.00 per share. If the Average Closing Price of
USB's common stock falls below $15.00 per share, the Registrant will have the
right to terminate the transaction subject to USB's right to adjust the Exchange
Ratio so as to assure the Registrant's shareholders receive a value of $18.60
per Registrant share.

     The transaction is intended to be a tax free exchange of common shares
(except cash received in lieu of fractional shares) and will be accounted for as
a pooling of interests. The transaction is subject to receipt of regulatory
approvals and the approval of the Registrant's shareholders. The transaction
will be presented for approval at a special meeting of the Registrant's
shareholders to be held on August 19, 1998 and a proxy statement relating to
this meeting has been mailed to all shareholders of record as of July 2, 1998.


                                       6
<PAGE>   8
      In connection with the Merger Agreement, the Registrant and USB also
entered into a Stock Option Agreement which, under certain defined
circumstances, would enable USB to purchase up to 294,134, or 19.9%, of the
Registrant's issued and outstanding common stock at a price of $18.50 per share.

     The unaudited consolidated financial statements included herein have been
prepared in conformity with generally accepted accounting principles. In the
opinion of management, the unaudited consolidated financial statements include
all adjustments, consisting of normal recurring accruals, necessary for a fair
presentation of the financial position and results of operations for the periods
presented. The results of operations for the three months ended June 30, 1998
are not necessarily indicative of the results of operations which may be
expected for the fiscal year ending March 31, 1999.

   Certain financial information and footnote disclosures normally included in
annual financial statements prepared in conformity with generally accepted
accounting principles have been condensed or omitted pursuant to the rules and
regulations of the Securities and Exchange Commission. The unaudited
consolidated financial statements presented herein should be read in conjunction
with the audited consolidated financial statements and notes thereto included in
the Company's Annual Report to Shareholders and Annual Report on Form 10-K for
the fiscal year ended March 31, 1998.

     Certain reclassifications have been made to conform the prior period's
consolidated financial statements to the current presentation.

(2)      Other Comprehensive Income

      During the quarter ended June 30, 1998, the Company adopted Statement of
Financial Accounting Standards ("SFAS") No. 130, "Reporting Comprehensive
Income". Total comprehensive income for the quarter ended June 30, 1998 was
$415,000. This consisted of $302,000 in net income and $113,000 in net
unrealized gains on available-for-sale securities, net of tax.

(3)       Earnings Per Share

       In fiscal 1998, the Company retroactively adopted SFAS No. 128, "Earnings
  Per Share," which established new standards for computing and presenting
  earnings per share ("EPS") by all entities with complex capital structures.
  SFAS No. 128 requires the presentation of basic EPS and diluted EPS and the
  restatement of all prior-period EPS data. Basic EPS excludes dilution and is
  computed by dividing net income available to common shareholders by the
  weighted average number of common shares outstanding for the period.
  Unallocated ESOP shares that have not been committed to be released to
  participants are excluded from outstanding shares in computing EPS. Diluted
  EPS reflects the potential dilution that could occur if securities or other
  contracts to issue common stock (such as the Company's stock options and RRP
  awards) were exercised or converted into common stock or resulted in the
  issuance of common stock. Diluted EPS is computed by dividing adjusted net
  income by the weighted average number of common shares outstanding for the
  period plus common stock equivalents. The following is an analysis of the
  Company's EPS computations under SFAS No. 128 for the three months ended June
  30, 1998 and 1997:


                                       7
<PAGE>   9
<TABLE>
<CAPTION>
                                                                       THREE MONTHS ENDED JUNE 30,
                                                                      ----------------------------
                                                                         1998             1997
                                                                      ----------       ----------
                                                             (Dollars in thousands, except per share data)
<S>                                                                   <C>              <C>       
BASIC EPS:
     Net income available to common shareholders                      $      302       $      265
                                                                      ----------       ----------

     Weighted average common shares outstanding                        1,346,670        1,365,571
                                                                      ----------       ----------

     Basic EPS                                                        $     0.22       $     0.19
                                                                      ==========       ==========

DILUTED EPS:
     Net income                                                       $      302       $      265
                                                                      ----------       ----------

     Weighted average common shares outstanding                        1,346,670        1,365,571
     Potential common stock equivalents (using the
       treasury method):                                                  74,969           43,020
                                                                      ----------       ----------
     Total weighted average diluted shares                             1,421,639        1,408,591
                                                                      ----------       ----------

     Diluted EPS                                                      $     0.21       $     0.19
                                                                      ==========       ==========
</TABLE>


(4)   Recent Accounting Pronouncements

     In June 1998, the Financial Accounting Standards Board issued SFAS No. 133
"Accounting for Derivative Instruments and Hedging Activities" (the "Statement"
or "SFAS No. 133"). The Statement establishes accounting and reporting standards
requiring derivative instruments to be recorded in the balance sheet, either as
an asset, or as a liability, measured at its fair value. The Statement requires
that changes in a derivative's fair value be recognized in current earnings
unless specific hedge accounting criteria are met. Special accounting for
qualifying hedges allows a derivative's gains and losses to offset related
results on the hedged item in the income statement, and requires that a company
must formally document, designate, and assess the effectiveness of transactions
that receive hedge accounting.

     SFAS No. 133 is effective for fiscal years beginning after June 15, 1999. A
company may also implement the Statement as of the beginning of any fiscal
quarter after issuance but cannot apply the Statement retroactively. SFAS No.
133 must be applied to derivative instruments and certain derivative instruments
embedded in hybrid contracts that were issued, acquired or substantively
modified after December 31, 1997.

     The Company does not currently have derivative or hedged instruments and
management does not anticipate the Statement having a material impact on its
financial position or results of operations.


                                       8
<PAGE>   10
ITEM 2.     MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
            AND RESULTS OF OPERATIONS.

GENERAL

     The Company's primary market area consists of the Village of Tarrytown and
its neighboring communities in Westchester County, New York with business
conducted from one office located in Tarrytown, New York. The Bank is a
community-oriented savings institution whose business primarily consists of
accepting deposits from customers within its market area and investing those
funds in mortgage loans secured by one- to four-family residences. To a
significantly lesser extent, funds are invested in multi-family, commercial real
estate, construction, commercial business and consumer loans. The Company also
invests in mortgage-backed and other securities. The Registrant has no
significant business activities other than its ownership of the Bank.

     The Company's results of operations are dependent primarily on net interest
income, which is the difference between the interest income earned on its
interest-earning assets, such as loans and securities, and the interest expense
on its interest-bearing liabilities, such as deposits. The Company also
generates non-interest income such as service charges and other fees. The
Company's non-interest expense consists of compensation and benefits,
professional service fees, occupancy expenses, federal deposit insurance costs,
data processing service fees and other operating expenses. The Company's results
of operations are significantly affected by general economic and competitive
conditions (particularly changes in market interest rates), government policies,
changes in accounting standards and actions of regulatory agencies.

MERGER AGREEMENT

     As discussed in note 1 of the unaudited consolidated financial statements,
on March 6, 1998, the Registrant entered into an Agreement and Plan of Merger
with U.S.B. Holding Co., Inc. ("USB") (the "Merger Agreement") pursuant to which
the Registrant will merge with and into USB, a registered bank holding company
and parent company of Union State Bank, a New York State chartered commercial
bank. The Bank will operate as a wholly-owned subsidiary of USB.

      The transaction is intended to be a tax free exchange of common shares and
 will be accounted for as a pooling of interests. The transaction is subject to
 receipt of regulatory approvals and approval of the Registrant's shareholders.

 YEAR 2000 COMPLIANCE

      The Company, like all companies that utilize computer technology, is
 facing significant challenges associated with the inability of computer systems
 to recognize the year 2000 (the "Year 2000 Problem"). Many existing computer
 programs and systems were originally programmed with six digit dates that
 provided only two digits to identify the calendar year in the date field,
 without considering the upcoming change in the century. With the impending
 millennium, these programs and computers will recognize "00" as the year 1900
 rather than the year 2000. Like most financial service providers, the Company
 and its operations may be significantly affected by the Year 2000 Problem due
 to the nature of financial information. Software, hardware, and equipment both


                                       9
<PAGE>   11
 within and outside the Company's direct control and with whom the Company
 electronically or operationally interfaces (e.g. third party vendors providing
 data processing, information system management, maintenance of computer
 systems, and credit bureau information) are affected. Furthermore, if computer
 systems are not adequately changed to identify the year 2000, many computer
 applications could fail or create erroneous results. As a result, many
 calculations which rely on the date field information, such as interest,
 payment or due dates and other operating functions, will generate results which
 could be significantly misstated, and the Company could experience a temporary
 inability to process transactions, send invoices or engage in similar normal
 business activities. In addition, under certain circumstances, failure to
 adequately address the Year 2000 Problem could adversely affect the viability
 of the Company's suppliers and creditors and the creditworthiness of its
 borrowers. Thus, if not adequately addressed, the Year 2000 Problem could
 result in a significant adverse impact on the Company's products, services and
 competitive condition.

      The Company is in communication with all of its significant suppliers to
 determine the extent to which the Company is vulnerable to those third parties'
 failure to remediate their own Year 2000 Problem. The Company presently
 believes that with modifications to existing software and conversions to new
 software, the Year 2000 Problem will be mitigated without causing a material
 adverse impact on the operations of the Company. However, if such modifications
 and conversions are not made, or are not completed timely, the Year 2000
 Problem could have an impact on the operations of the Company. At this time,
 management does not believe that the impact and any resulting costs will be
 material.

      Monitoring and managing the Year 2000 Problem will result in additional
direct and indirect costs to the Company. Direct costs include potential charges
by third party software vendors for product enhancements, costs involved in
testing software products for year 2000 compliance, and any resulting costs for
developing and implementing contingency plans for critical software products
which are not enhanced. Indirect costs will principally consist of the time
devoted by existing employees in monitoring software vendor progress, testing
enhanced software products and implementing any necessary contingency plans. To
date, the Company has not incurred significant costs in remediating the Year
2000 Problem and does not expect additional costs to have a material effect on
its results of operations. Both direct and indirect costs of addressing the Year
2000 Problem are charged to earnings as incurred.

LIQUIDITY AND CAPITAL RESOURCES

     The Company's primary sources of funds are deposits, principal and interest
payments on loans and securities and, to a lesser extent, advances from the
Federal Home Loan Bank ("FHLB") of New York and proceeds from the sale of
securities. While maturities and scheduled amortization of loans and securities
provide an indication of the timing of the receipt of funds, changes in interest
rates, economic conditions, and competition strongly influence mortgage
prepayment rates and deposit flows, reducing the predictability of the timing of
these cash flows.

    The Bank is required to maintain an average daily balance of liquid assets
as a percentage of net withdrawable deposit accounts plus short-term borrowings
as defined by the regulations of the Office of Thrift Supervision ("OTS"). The
minimum required liquidity ratio is currently 5.0%. At June 30, 1998 and March
31, 1998, the Company's 


                                       10
<PAGE>   12
liquidity ratio was 70.6% and 58.5%, respectively. The levels of the Company's
short-term liquid assets are dependent on the Company's operating, financing and
investing activities during any given period.

    The Company's cash flows are derived from operating activities, investing
activities and financing activities. Cash flows from operating activities
consist primarily of interest income received and interest expense paid. Net
cash flows from investing activities consist primarily of loan originations and
payments (including amortization of principal and prepayments) and the purchase,
maturity and sale of securities, including mortgage-backed securities. Financing
activity cash flows are generated primarily from deposit activity. The Company
has other sources of liquidity if a need for additional funds arises, including
borrowing capacity from the FHLB of New York of up to 25% of the Bank's assets,
which amounts to $33.9 million at June 30, 1998. At June 30, 1998 such
borrowings amounted to $10.0 million. The utilization of particular sources of
funds depends on comparative costs and availability.

     At June 30, 1998, the Company had outstanding loan origination commitments
of $1.5 million, undisbursed construction loans in process of $104,000 and
unadvanced commercial lines of credit of $15,000. The Company anticipates that
it will have sufficient funds available to meet its current origination and
other lending commitments. Certificates of deposit scheduled to mature in one
year or less from June 30, 1998 totaled $55.1 million with a weighted average
rate of 5.68%. Based upon the Company's most recent experience and pricing
strategy, management believes that a significant portion of such deposits will
remain with the Bank.

   The main source of liquidity for the Registrant is dividends from the Bank.
The Registrant may access capital markets through the issuance of stock or debt
for additional sources of funds. The main cash outflows are payments of
dividends to shareholders and repurchases of the Registrant's common stock.
Through June 30, 1998, the Registrant has repurchased for its treasury 142,000
shares of its common stock, or 8.8% of the shares issued in the Registrant's
initial public offering at an aggregate cost of $2.1 million. The Registrant's
ability to pay dividends to shareholders depends substantially on dividends
received from the Bank. The Bank may not declare or pay cash dividends on its
common stock if the effect thereof would cause equity to be reduced below
applicable regulatory capital requirements or the amount required to be
maintained for the liquidation account established in connection with the
conversion of the Bank from mutual to stock form. Unlike the Bank, the
Registrant is not subject to OTS regulatory restrictions on the payment of
dividends to its shareholders, however, it is subject to the requirements of
Delaware law. The Delaware General Corporation Law generally limits dividends to
an amount equal to the excess of the net assets of the Registrant (the amount by
which total assets exceed total liabilities) over its statutory capital, or if
there is no such excess, to its profits for the current and/or immediately
preceding fiscal year.

    OTS regulations require savings associations, such as the Bank, to maintain
a minimum capital ratio of tangible capital to total adjusted assets of 1.5%; a
minimum ratio of Tier I (core) capital to total adjusted assets of 4%; a minimum
ratio of Tier I (core) capital to total risk-weighted assets of 4%; and a
minimum ratio of total (core and supplementary) capital to total risk-weighted
assets of 8%. At June 30, 1998, the Bank satisfied these minimum capital
standards and was classified as a "well capitalized" institution.


                                       11
<PAGE>   13
     The following is a summary of the Bank's actual capital amounts and ratios
as of June 30 and March 31, 1998, compared to the OTS regulatory requirements
for classification as well as a well-capitalized institution and for minimum
capital adequacy:

<TABLE>
<CAPTION>
                                                     For Classification as        Minimum Capital
                               Bank Actual            Well Capitalized                Adequacy
                            ------------------       -------------------       --------------------
                            Amount       Ratio       Amount        Ratio       Amount         Ratio
                            ------       -----       ------        -----       ------         -----
                                                   (Dollars in thousands)
June 30, 1998
<S>                        <C>           <C>         <C>           <C>         <C>            <C>
Tangible capital           $17,452       12.9%           N/A        N/A        $ 2,029        1.5%
Tier I (core) capital       17,452       12.9        $ 6,763        5.0%       $ 5,411        4.0
Risk-based capital:
     Tier I                 17,452       43.9          2,387        6.0        $ 1,591        4.0
     Total                  17,952       45.1          3,978       10.0          3,182        8.0


March 31, 1998
Tangible capital           $17,292       13.8%           N/A        N/A        $ 1,878        1.5%
Tier I (core) capital       17,292       13.8        $ 6,259        5.0%       $ 5,007        4.0
Risk-based capital:
     Tier I                 17,292       43.3          2,394        6.0          1,596        4.0
     Total                  17,793       44.6          3,989       10.0          3,191        8.0
</TABLE>


    In determining the amount of risk-weighted assets for purposes of the
risk-based capital requirement, a savings association multiplies its assets and
certain off-balance sheet items by risk-weights, which range from 0% for cash
and obligations issued by the United States Government or its agencies to 100%
for consumer and commercial loans, as assigned by the OTS capital regulations.
These capital requirements, which are applicable to the Bank only, do not
consider additional capital held at the holding company level, and require
certain adjustments to Bank's total equity to arrive at the various regulatory
capital amounts.

COMPARISON OF FINANCIAL CONDITION AT JUNE 30, 1998 AND MARCH 31, 1998

     Total assets at June 30, 1998 increased $10.4 million, to $139.7 million
from $129.3 million at March 31, 1998. This increase was primarily the result of
an increase in the securities portfolio of $12.3 million to $70.7 million at
June 30, 1998 from $58.4 million at March 31, 1998 partially offset by decreases
of $700,000, $1.1 million and $721,000 in federal funds sold, interest-bearing
deposits and loans, net, respectively. Loans, net, totaled $56.9 million at June
30, 1998, compared to $57.6 million at March 31, 1998. Within the securities
portfolio, mortgage-backed securities totaled $68.5 million at June 30, 1998
compared to $53.1 million at March 31, 1998. The growth in the securities
portfolio was funded primarily by Federal Home Loan Bank ("FHLB") advances which
amounted to $10.0 million at June 30, 1998. There were no such borrowings at
March 31, 1998. Deposits amounted to $105.2 million at June 30, 1998, an
increase of $229,000 from $105.0 million at March 31, 1998.


                                       12
<PAGE>   14
     Shareholders' equity was $22.1 million at June 30, 1998, an increase of
$335,000 from $21.8 million at March 31, 1998. The increase primarily reflects
net earnings retained after dividends of $205,000, an increase of $106,000
relating to the employee stock ownership plan ("ESOP") and the recognition and
retention plans ("RRPs") and a $24,000 increase in the net unrealized gain on
available-for-sale securities. The ratio of shareholders' equity to total assets
at June 30, 1998 was 15.85%, as compared to 16.85% at March 31, 1998. The
Company's tangible book value per share was $14.98 at June 30, 1998 compared to
$14.75 at March 31, 1998.


                                       13
<PAGE>   15
ANALYSIS OF NET INTEREST INCOME

    The following table sets forth the Company's average balance sheets, average
yields and costs (on an annualized basis), and certain other information for the
three months ended June 30, 1998 and 1997. The yields and costs were derived by
dividing interest income or expense by the average balance of assets or
liabilities, respectively, for the periods shown. Substantially all average
balances were computed based on month-end balances, producing results which
approximate average daily balances. Interest income includes the effect of
deferred fees and discounts which are considered yield adjustments.

<TABLE>
<CAPTION>
                                                                             FOR THE QUARTER ENDED JUNE 30,
                                                 ---------------------------------------------------------------------------------
                                                                1998                                         1997
                                                 ---------------------------------------------------------------------------------
                                                    AVERAGE                 AVERAGE          AVERAGE                       AVERAGE
                                                    BALANCE    INTEREST       RATE           BALANCE       INTEREST          RATE
                                                 ---------     ---------    --------       ---------       ---------       -------
ASSETS:                                                                        (DOLLARS IN THOUSANDS)
<S>                                              <C>           <C>          <C>            <C>             <C>             <C> 
    Interest-earning assets:
      Loans (1)                                  $  57,860     $   1,236       8.54%       $  56,347       $   1,199         8.51%
      Mortgage-backed securities (2)                60,665         1,084       7.15           38,761             704         7.27
      Other securities (2)                           3,123            51       6.53           11,756             190         6.46
      Federal funds sold                             5,667            75       5.29           11,477             151         5.26
      FHLB stock                                       943            17       7.21              674              10         5.93
      Other                                          1,931            14       2.90              880              11         5.00
                                                 ---------     ---------                   ---------       ---------         
        Total interest-earning assets              130,189     $   2,477       7.61%         119,895       $   2,265         7.56%
                                                               =========                                   =========         
    Allowance for loan losses                         (705)                                     (665)
    Non-interest-earning assets                      4,314                                     3,649
                                                 ---------                                 ---------
        Total assets                             $ 133,798                                 $ 122,879
                                                 =========                                 =========
LIABILITIES AND EQUITY:
    Interest-bearing liabilities:
      NOW and money market                       $   7,009     $      38       2.17%       $   6,793       $      39         2.30%
      Savings accounts                              25,093           178       2.84           25,454             179         2.81
       FHLB advance                                  4,555            69       6.05               --              --           --
      Certificate accounts and other                71,015           996       5.61           65,217             914         5.61
                                                   -------     ---------                      ------       ---------
       Total interest-bearing liabilities          107,672     $   1,281       4.76%          97,464       $   1,132         4.65%
                                                               =========                                   =========
    Checking accounts                                2,530                                     2,598
    Other non-interest-bearing liabilities           1,640                                     1,548
                                                   -------                                    ------                    
        Total liabilities                          111,842                                   101,610
    Equity                                          21,956                                    21,269
                                                   -------                                    ------                    
        Total liabilities and equity             $ 133,798                                 $ 122,879
                                                 =========                                 =========
Net interest income                                            $   1,196                                   $   1,133
                                                               =========                                   =========
Average interest rate spread (3)                                               2.85%                                       2.91%
Net interest margin (4)                                                        3.67                                        3.78
Ratio of interest-earning assets to
  interest-bearing liabilities                     120.91%                                   123.01%
</TABLE>


(1)  Balances are net of deferred loan fees, loan discounts and premiums, and
     loans in process. Non-accrual loans are included in the balances.

(2)  Balances represent amortized cost.

(3)  Average interest rate spread represents the difference between the yield on
     average interest-earning assets and the cost of average interest-bearing
     liabilities.

(4)  Net interest margin represents net interest income divided by average total
     interest-earning assets.


                                       14
<PAGE>   16
     The following table presents the extent to which changes in interest rates
and changes in the volume of interest-earning assets and interest-bearing
liabilities affected the Company's interest income and interest expense during
the three months ended June 30, 1998 compared to the same period in the prior
year. Information is provided in each category with respect to (i) changes
attributable to changes in volume (changes in volume multiplied by prior rate),
(ii) changes attributable to changes in rate (changes in rate multiplied by
prior volume), and (iii) the net change. The changes attributable to the
combined impact of volume and rate have been allocated proportionately to the
changes due to volume and the changes due to rate.
<TABLE>
<CAPTION>
                                                          FISCAL 1999 VS. 1998                     FISCAL 1998 VS. 1997
                                                   ---------------------------------       ---------------------------------
                                                   INCREASE (DECREASE)                     INCREASE (DECREASE)
                                                       DUE TO                 NET                DUE TO               NET
                                                   ------------------                      ------------------
                                                   VOLUME        RATE        CHANGE        VOLUME        RATE        CHANGE
                                                   ------        ----        ------        ------        ----        ------
                                                                                (IN THOUSANDS)
<S>                                                <C>           <C>         <C>           <C>           <C>         <C> 
Interest-earning assets:
  Loans                                             $ 33          $ 4         $ 37          $ 65         $ (8)        $ 57
  Mortgage-backed securities                         392          (12)         380            26           40           66
  Other securities                                  (141)           2         (139)          (44)          12          (32)
  Federal funds sold                                 (77)           1          (76)          101           (5)          96
  FHLB stock                                           5            2            7             2           (1)           1
  Other                                                9           (6)           3           (11)           -          (11)
                                                    ----         ----         ----          ----         ----         ----
            Total                                    221           (9)         212           139           38          177
                                                    ----         ----         ----          ----         ----         ----

Interest-bearing liabilities
  NOW and money market accounts                        1           (2)          (1)           (1)          (1)          (2)
  Savings accounts                                    (3)           2           (1)          (17)         (22)         (39)
  Certificate accounts and other                      82           --           82           163            9          172
  Short term FHLB borrowings                          69           --           69            (3)           -           (3)
                                                    ----         ----         ----          ----         ----         ----
            Total                                    149           --          149           142          (14)         128
                                                    ----         ----         ----          ----         ----         ----

Net change in net interest income                   $ 72         $ (9)        $ 63          $ (3)        $ 52         $ 49
                                                    ====         ====         ====          ====         ====         ====
</TABLE>

COMPARISON OF OPERATING RESULTS FOR THE THREE MONTHS ENDED JUNE 30, 1998 AND
JUNE 30, 1997

     General. Net income for the quarter ended June 30, 1998 was $302,000, or
$0.22 basic earnings per share ($0.21 diluted earnings per share), compared with
$265,000, or $0.19 basic earnings per share ($0.19 diluted earnings per share)
for the comparable period in 1997. Net interest income for the three months
ended June 30, 1998 increased $63,000 and non-interest expense increased $15,000
from the 1997 quarter. The return on average assets and return on average equity
were 0.90% and 5.50%, respectively, for the three months ended June 30, 1998,
compared to 0.86% and 4.98%, respectively, for the 1997 quarter.

     Net Interest Income. Net interest income for the three months ended June
30, 1998 amounted to $1.2 million as compared to $1.1 million for the same
period last year. The increase is primarily due to higher average
interest-earning assets, partially offset by a lower interest rate spread. The
Company's average interest rate spread decreased to 2.85% for the quarter ended
June 30, 1998, compared to 2.91% for the quarter ended June 30, 1997. The
Company's net interest margin decreased to 3.67% for the quarter ended June 30,
1998, as compared to 3.78% for the quarter ended June 30, 1997. The decreases in


                                       15
<PAGE>   17
spread and margin are due primarily to the increases in the average balance of
certificates of deposit and borrowings from the FHLB.

     Interest Income. Interest income, which amounted to $2.5 million for the
quarter ended June 30, 1998, increased $212,000, or 9.4%, compared to the
quarter ended June 30, 1997. This increase is primarily due to a $10.3 million
increase in average interest-earning assets funded by deposit growth and
advances from the Federal Home Loan Bank. The overall increase in average
interest-earning assets reflects increases of $21.9 million in the average
mortgage-backed securities portfolio and $1.5 million in the average loan
portfolio, partially offset by a $8.6 million decrease in the average other
securities portfolio and $4.5 million decrease in other earning assets
(principally federal funds sold). The increase in the average balance of
mortgage-backed securities reflects management's efforts to invest proceeds from
the payment of other securities and earning assets and increased deposit flow
and borrowed funds from leveraging of the Company's capital base into
mortgage-backed securities. The increase in the average yield on
interest-earning assets, to 7.61% for the quarter ended June 30, 1998 from 7.56%
for the same period in 1997, primarily reflects this shift in investments to
higher yielding fixed rate mortgage-backed securities.

     Interest Expense. Interest expense for the quarter ended June 30, 1998
amounted to $1.3 million, an increase of $149,000, or 13.2%, from the quarter
ended June 30, 1997. This increase is primarily attributable to a $10.2 million
increase in average interest-bearing liabilities due to an increase in the
average balance of certificates of deposit and advances from the FHLB. The FHLB
advance has an amortizing term of seven years, financed the purchase of GNMA
mortgage-backed securities and is expected to produce a positive spread of
approximately 70 basis points. The average cost of funds for the three months
ended June 30, 1998 was 4.76% as compared to 4.65% for the 1997 quarter. The
higher cost of funds relates primarily to the increased volume in certificates
of deposit and borrowed funds.

     Provision for Loan Losses. The provision for loan losses was $10,000 for
the quarter ended June 30, 1998, compared to $11,000 for the quarter ended June
30, 1997. The provision in each period reflects management's evaluation of the
adequacy of the allowance for loan losses. Factors considered include the
Company's previous loan loss experience, the known and inherent risks in the
loan portfolio, adverse situations that may affect the borrowers' ability to
repay, the estimated value of any underlying collateral, and current economic
conditions. Non-performing loans amounted to $1.5 million at June 30, 1998 as
compared to $1.6 million at March 31, 1998 and $2.0 million a year earlier. See
"-- Asset Quality".

     Non-Interest Income. Non-interest income was $42,000 and $50,000 for the
three months ended June 30, 1998 and 1997, respectively. The reduction in
non-interest income is attributable to the absence of gains on sales of
available-for-sale securities in the current period compared with $11,000 in
such gains reported in the comparable quarter.

     Non-Interest Expense. Non-interest expense amounted to $729,000 for the
quarter ended June 30, 1998, reflecting an increase of $15,000 from the 1997
quarter, primarily due to increases in compensation and benefits of $36,000,
partially offset by a reduction


                                       16
<PAGE>   18
of $17,000 in professional services. The increase in compensation and benefits
expense is primarily attributable to performance-based increases for certain
staff members coupled with the increased recognition of expense associated with
the ESOP due to the higher average stock price of the Company in the current
quarter as compared to the prior year's quarter. The ratio of non-interest
expense to average assets, on an annualized basis, decreased to 2.18% for the
quarter ended June 30, 1998 from 2.32% for the quarter ended June 30, 1997.

     Income Tax Expense. Income tax expense increased to $197,000 for the
quarter ended June 30, 1998, from $193,000 for the 1997 quarter, reflecting the
increase in pre-tax income. The effective income tax rates for the three months
ended June 30, 1998 and 1997 were 39.5% and 42.1%, respectively.

ASSET QUALITY

     Non-performing loans totaled $1.5 million at June 30, 1998, as compared to
$1.6 million at March 31, 1998 and $2.0 million at June 30, 1997. The decrease
was primarily due to the decrease in non-accruing loans secured by one-to
four-family residences. It is the Company's general policy to stop the accrual
of interest on all loans ninety days or more past due. Certain loans ninety days
or more past due may continue to accrue interest based on management's
evaluation of the loan, the underlying collateral and the credit worthiness of
the borrower. The allowance for loan losses was $708,000 at June 30, 1998,
compared to $702,000 at March 31, 1998 and $671,000 at June 30, 1997. The ratio
of non-performing loans to total loans was 2.68% at June 30, 1998 compared to
2.67% at March 31, 1998 and 3.56% at June 30, 1997. The ratio of non-performing
assets to total assets was 1.11% at June 30, 1998 compared to 1.21% at March 31,
1998 and 1.73% at June 30, 1997.


                                       17
<PAGE>   19
   The following table sets forth certain asset quality data at the dates
indicated:




<TABLE>
<CAPTION>
                                                                  JUNE 30,       MARCH 31,    JUNE 30,
                                                                    1998            1998       1997
                                                                  --------       ---------    -------
                                                                           (DOLLARS IN THOUSANDS)
<S>                                                                <C>           <C>          <C>   
NON-ACCRUAL LOANS:
  Mortgage loans:
     One-to four-family                                            $1,030        $1,202       $1,352
     Commercial property                                              238           238          120
                                                                   ------        ------       ------
      Total                                                         1,268         1,440        1,472
                                                                   ------        ------       ------
  Number of non-accrual loans                                           5             6            9

ACCRUING LOANS PAST DUE NINETY DAYS OR MORE: 
  Mortgage loans:
     One-to four-family                                            $   --        $   --       $  299
     Commercial property                                               --            --          248
     Multi-family property                                            261            --           --
     Construction                                                      --           108           --
  Commercial business and consumer                                     17            11            5
                                                                   ------        ------       ------
      Total                                                           278           119          552
                                                                   ------        ------       ------
  Number of accruing loans past due ninety days or more                 4             3            3

Total non-performing loans                                         $1,546        $1,559       $2,024
                                                                   ======        ======       ======
Number of non-performing loans                                          9             9           12

Allowance for loan losses                                          $  708        $  702       $  671
                                                                   ======        ======       ======

Real estate owned, net                                             $   --        $   --       $  122
                                                                   ======        ======       ======
Number of real estate owned properties                                 --            --            1

RATIOS:
  Non-accrual loans to total loans                                   2.20%         2.47%        2.59%
  Non-performing loans to total loans                                2.68          2.67         3.56
  Non-performing loans and real estate owned to total assets         1.11          1.21         1.73
  Allowance for loan losses to:
      Non-accrual loans                                             55.84         48.75        45.58
      Non-performing loans                                          45.80         45.03        33.15
      Total loans                                                    1.23          1.20         1.18
</TABLE>



ITEM 3.    QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK.

     Market risk is the potential loss from adverse changes in market prices and
rates. The Company's market risk arises primarily from interest rate risk
inherent in its lending, investing and deposit taking activities. The Company's
real estate loan portfolio, concentrated primarily in Westchester County, New
York, is subject to risks associated with the local economy.


                                       18
<PAGE>   20
      Since there have been no significant changes in the Company's balance
sheet or the yield curve subsequent March 31, 1998, the Company's current
interest rate risk exposure has not materially changed from that disclosed as of
March 31, 1998.


                         PART II - OTHER INFORMATION

ITEM 1.     LEGAL PROCEEDINGS.

     The Company is not involved in any pending legal proceedings other than
routine legal proceedings occurring in the ordinary course of business. Such
routine legal proceedings in the aggregate are believed by management to be
immaterial to the Company's financial condition and results of operations.

ITEM 2.     CHANGES IN SECURITIES.

     Not applicable.

ITEM 3.     DEFAULTS UPON SENIOR SECURITIES.

     Not applicable.

ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

     None.

ITEM 5.    OTHER INFORMATION

     None.

ITEM 6.    EXHIBITS AND REPORTS ON FORM 8-K

     (a)  Exhibits

            27.  Financial Data Schedule (submitted only with filing in
                 electronic format)

     (b)  Reports on Form 8-K

            None.


                                       19
<PAGE>   21
CONFORMED
                                 SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunder duly authorized.

                                         Tappan Zee Financial, Inc.

Dated:  August 14, 1998                  By:   /s/ Stephen C. Byelick
                                              -----------------------
                                         Stephen C. Byelick
                                         President and Chief Executive Officer


Dated:  August 14, 1998                   By:   /s/ Harry G. Murphy
                                               --------------------
                                         Harry G. Murphy
                                         Vice President & Secretary
                                         (principal financial officer)


                                       20