EXHIBIT 4.1


                          BRIDGE STREET FINANCIAL, INC.
                                STOCK OPTION PLAN
                       CONVERSION STOCK OPTION CERTIFICATE
                       -----------------------------------


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NAME OF OPTIONEE                                          SOCIAL SECURITY NUMBER

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                                 STREET ADDRESS

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CITY                                 STATE                              ZIP CODE

This Conversion Stock Option Agreement is intended to set forth the terms and
conditions on which a Stock Option has been granted under the Oswego County
Bancorp, Inc. Stock Option Plan and has been converted to be a Stock Option
under the Bridge Street Financial, Inc. Stock Option Plan. Set forth below are
the specific terms and conditions applicable to this Stock Option. Attached as
Exhibit A are its general terms and conditions.

<TABLE>
<CAPTION>
       Oswego Option Grant               (A)               (B)               (C)                (D)               (E)
<S>                                     <C>               <C>               <C>               <C>               <C>
                      Grant Date:
        Class of Optioned Shares*       Common            Common            Common            Common            Common
          No. of Optioned Shares*
        Exercise Price Per Share*
        Option Type (ISO or NQSO)
             VESTING
          Earliest Exercise Date*
          Option Expiration Date*

   Bridge Street Option Grant            (A)               (B)               (C)                (D)               (E)
        Class of Optioned Shares*       Common            Common            Common            Common            Common
          No. of Optioned Shares*
        Exercise Price Per Share*
        Option Type (ISO or NQSO)
             VESTING
          Earliest Exercise Date*
          Option Expiration Date*
</TABLE>

*SUBJECT TO ADJUSTMENT AS PROVIDED IN THE PLAN AND THE GENERAL TERMS AND
CONDITIONS.

By signing where indicated below, Bridge Street Financial, Inc. (the "Company")
grants this Stock Option upon the specified terms and conditions, and the
Optionee acknowledges receipt of this Conversion Stock Option Agreement,
including Exhibit A, and agrees to observe and be bound by the terms and
conditions set forth herein and acknowledges receipt of a Prospectus dated
January 3, 2003 for the Bridge Street Financial, Inc. Stock Option Plan.

BRIDGE STREET FINANCIAL, INC.                   OPTIONEE


By __________________________________           ________________________________
   NAME:
   TITLE:


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INSTRUCTIONS: This page should be completed by or on behalf of the Personnel and
Compensation Committee. Any blank space intentionally left blank should be
crossed out. An option grant consists of a number of optioned shares with
uniform terms and conditions. Where options are granted on the same date with
varying terms and conditions (for example, varying exercise prices or earliest
exercise dates), the options should be recorded as a series of grants each with
its own uniform terms and conditions.

<PAGE>

                                                                       EXHIBIT A
                                                                       ---------

                 BRIDGE STREET FINANCIAL, INC. STOCK OPTION PLAN
                       CONVERSION STOCK OPTION CERTIFICATE
                       -----------------------------------

                          GENERAL TERMS AND CONDITIONS

         SECTION 1. OPTION SIZE AND TYPE. The number of shares of Common Stock,
par value $.01 per share ("Shares"), that have been optioned to you under the
Bridge Street Financial, Inc. Stock Option Plan (the "Plan") is specified in
this Conversion Stock Option Certificate. If the "Option Type" shown for your
stock option is "ISO", then your stock option has been designed with the intent
that it qualify to the maximum permissible extent for the special tax benefits
applicable to incentive stock options under the Internal Revenue Code of 1986.
If the "Option Type" shown for your stock options is "NQSO", then incentive
stock option tax treatment is not applicable.

         SECTION 2. EXERCISE PRICE. The Exercise Price for your stock options is
the price per Share at which you may acquire the Shares that have been optioned
to you and is specified in this Conversion Stock Option Certificate. As a
general rule, the Exercise Price for your stock options will not change unless
there is a stock split, stock dividend, merger or other major corporate event
that justifies an adjustment.

         SECTION 3.  VESTING.

                  (a) EARLIEST EXERCISE DATE. You may not exercise your stock
         options until they are vested. The date on which your stock options
         become vested is specified in this Conversion Stock Option Certificate
         as the Earliest Exercise Date. As a general rule, you must be in the
         service of the Company on an Earliest Exercise Date in order to be
         vested in the stock options that vest on that date. You may acquire the
         Shares that have been optioned to you by exercising your stock options
         at any time during the period beginning on the Earliest Exercise Date
         and continuing until the applicable Option Expiration Date, by
         completing and filing the Notice of Exercise of Stock Option that is
         attached to this Conversion Stock Option Certificate as Appendix A and
         by following the procedures outlined therein.

                  (b) FORFEITURES. If you terminate service with the Company
         prior to an Earliest Exercise Date, you will forfeit any stock options
         that are scheduled to vest on that date. When you forfeit stock
         options, you relinquish any and all rights that you have to acquire the
         Shares that were optioned to you.

                  (c) ACCELERATED VESTING. All of your outstanding stock options
         that have not previously vested will become fully and immediately
         vested, without any further action on your part, in the event of your
         death or Disability (as defined in the Plan) or Change of Control (as
         defined in the Plan) before your termination of service with the
         Company or if your service terminates due to Retirement (as defined in
         the Plan). If vesting accelerates, the accelerated vesting date will be
         the applicable Earliest Exercise Date. You may designate a beneficiary
         to inherit your rights to any vested, unexercised stock options that
         are outstanding to you at your death using the Beneficiary Designation
         attached as Appendix B.

         SECTION 4. OPTION EXPIRATION DATE. To derive any benefit from your
stock options, you must exercise them during the period that begins on the
applicable Earliest Exercise Date and ends on the Option Expiration Date. The
Option Expiration Date for your stock options is specified in this Conversion
Stock Option Certificate. Your Option Expiration Date may be accelerated in the
event of your termination of service with the Company as follows:

                  (a) OPTIONS GRANTED TO ELIGIBLE EMPLOYEES. Your stock options
         will expire on the earliest of (i) the Option Expiration Date, (ii)
         three months after your termination of service with the Company for any
         reason other than death, Disability (as defined in the Plan),
         Retirement (as defined in the Plan), or Termination for Cause (as
         defined in the Plan); (iii) one year after your termination of service
         due to death or Disability; and (iv) the date and time of your
         Termination for Cause.

                  (b) OPTIONS GRANTED TO OUTSIDE DIRECTORS. Your stock options
         will expire on the earlier of (i) the Option Expiration Date and (ii)
         the date and time of your removal as a director for cause under the
         Company's By-laws.

To qualify for the favorable tax treatment accorded to incentive stock options,
you (or, in the event of your death, your estate or designated beneficiaries)
must exercise any stock options that are designated as ISOs within three months
after you terminate service as a common-law employee of the Company and its
subsidiaries for any reason other than death or disability and within one year
after you terminate service as common-law employee due to your death or
disability. If they are exercised later, they will be subject to tax as if they
were designated as NQSOs.

         SECTION 5. AMENDMENT. This Certificate may be amended, in whole or in
part and in any manner not inconsistent with the provisions of the Plan, at any
time and from time to time, by written Certificate between the Company and you.

         SECTION 6. PLAN PROVISIONS CONTROL. This Certificate and the rights and
obligations created hereunder shall be subject to all of the terms and
conditions of the Plan. In the event of any conflict between the provisions of
the Plan and the provisions of this Certificate, the terms of the Plan, which
are incorporated herein by reference, shall control. Capitalized terms in this
Certificate have the meaning defined in the Plan, as amended from time to time,
unless stated otherwise. By signing this Certificate, you acknowledge receipt of
a copy of the Plan and a copy of the related Prospectus dated January 3, 2003.


<PAGE>


                APPENDIX A TO CONVERSION STOCK OPTION CERTIFICATE
                 BRIDGE STREET FINANCIAL, INC. STOCK OPTION PLAN
                       NOTICE OF EXERCISE OF STOCK OPTION

USE THIS NOTICE TO INFORM BRIDGE STREET FINANCIAL, INC. THAT YOU ARE EXERCISING
YOUR RIGHT TO PURCHASE SHARES OF COMMON STOCK ("SHARES") OF BRIDGE STREET
FINANCIAL, INC. PURSUANT TO AN OPTION ("OPTION") GRANTED UNDER THE BRIDGE STREET
FINANCIAL, INC. STOCK OPTION PLAN ("PLAN"). IF YOU ARE NOT THE PERSON TO WHOM
THE OPTION WAS GRANTED ("OPTION RECIPIENT"), YOU MUST ATTACH TO THIS NOTICE
PROOF OF YOUR RIGHT TO EXERCISE THE OPTION GRANTED UNDER THE STOCK OPTION
CERTIFICATE ENTERED INTO BETWEEN BRIDGE STREET FINANCIAL, INC. AND THE OPTION
RECIPIENT ("CERTIFICATE"). THIS NOTICE SHOULD BE PERSONALLY DELIVERED OR MAILED
BY CERTIFIED MAIL, RETURN RECEIPT REQUESTED TO: BRIDGE STREET FINANCIAL, INC.,
44 EAST BRIDGE STREET, OSWEGO, NEW YORK 13126, ATTENTION: CORPORATE SECRETARY.
THE EFFECTIVE DATE OF THE EXERCISE OF THE OPTION SHALL BE THE EARLIEST DATE
PRACTICABLE FOLLOWING THE DATE THIS NOTICE IS RECEIVED BY BRIDGE STREET
FINANCIAL, INC. BUT IN NO EVENT MORE THAN THREE DAYS AFTER SUCH DATE ("EFFECTIVE
DATE"). EXCEPT AS SPECIFICALLY PROVIDED TO THE CONTRARY HEREIN, CAPITALIZED
TERMS SHALL HAVE THE MEANINGS ASSIGNED TO THEM UNDER THE PLAN.

OPTION INFORMATION      IDENTIFY BELOW THE OPTION THAT YOU ARE EXERCISING BY
                        PROVIDING THE FOLLOWING INFORMATION FROM THE CONVERSION
                        STOCK OPTION CERTIFICATE.

<TABLE>
<CAPTION>
<S>                                                                                  <C>
         NAME OF OPTION RECIPIENT: _____________________________________________

         OPTION GRANT DATE:        _______________________ _________________         EXERCISE PRICE PER SHARE:  $____________._____
                                     (MONTH AND DAY)            (YEAR)
</TABLE>

EXERCISE PRICE          COMPUTE THE EXERCISE PRICE BELOW AND SELECT A METHOD OF
                        PAYMENT.

<TABLE>
<CAPTION>
<S>                                 <C>                                     <C>                       <C>
         TOTAL EXERCISE PRICE       _________________________________    x  $_______________.____  =  $_____________________________
                                            (No. of Shares)                     (Exercise Price)            Total Exercise Price
</TABLE>

<TABLE>
<CAPTION>
         METHOD OF PAYMENT

<S>               <C>                                                                                           <C>
                  | | I enclose a certified check, money order, or bank draft payable to the order of Bridge
                      Street Financial, Inc. in the amount of                                                   $___________________

                  | | I enclose Shares I have owned for at least six months duly endorsed for transfer to
                      Bridge Street Financial, Inc. with all stamps attached and having a fair market value of  $___________________

                      Total Exercise Price                                                                      $___________________
</TABLE>

         *SUBJECT TO COMMITTEE APPROVAL AS AN ACCEPTABLE METHOD OF PAYMENT.

ISSUANCE OF CERTIFICATES

     I hereby direct that the stock certificates representing the Shares
     purchased above be issued to the following person(s) in the amount
     specified below:

<TABLE>
<CAPTION>
                             NAME AND ADDRESS                                        SOCIAL SECURITY NO.             NO. OF SHARES
<S>                                                                                  <C>                             <C>

_______________________________________________________________________

_______________________________________________________________________   ___________-__________-_______________     _______________

_______________________________________________________________________

_______________________________________________________________________   ___________-__________-_______________     _______________
</TABLE>

WITHHOLDING ELECTIONS   FOR EMPLOYEE OPTION RECIPIENTS WITH NON-QUALIFIED STOCK
                        OPTIONS ONLY. BENEFICIARIES AND OUTSIDE DIRECTORS SHOULD
                        NOT COMPLETE.

     I understand that I am responsible for the amount of federal, state and
     local taxes required to be withheld with respect to the Shares to be issued
     to me pursuant to this Notice, but that I may request Bridge Street
     Financial, Inc. to retain or sell a sufficient number of such Shares to
     cover the amount to be withheld. I hereby request that any taxes required
     to be withheld be paid in the following manner [check one]:

           | |  With a certified or bank check that I will deliver to the Bridge
                Street Financial, Inc. on the day after the Effective Date of my
                Option exercise.

           | |  With the proceeds from a sale of Shares that would otherwise be
                distributed to me.

           | |  Retain shares that would otherwise be distributed to me and that
                have a value equal to the minimum amount required to be withheld
                by law.

     I understand that the withholding elections I have made on this form are
     not binding on the Committee, and that the Committee will decide the amount
     to be withheld and the method of withholding and advise me of its decision
     prior to the Effective Date. I further understand that the Committee may
     request additional information or assurances regarding the manner and time
     at which I will report the income attributable to the distribution to be
     made to me. I further understand that if I have elected to have Shares sold
     to satisfy tax withholding, I may be asked to pay a minimal amount of such
     taxes in cash in order to avoid the sale of more Shares than are necessary.

COMPLIANCE WITH TAX AND SECURITIES LAWS

S    H          I understand that I must rely on, and consult with, my own tax
                and legal counsel (and not Bridge Street Financial, Inc.)
I    E          regarding the application of all laws -- particularly tax and
                securities laws -- to the transactions to be effected pursuant
G    R          to my Option and this Notice. I understand that I will be
                responsible for paying any federal, state and local taxes that
N    E          may become due upon the sale (including a sale pursuant to a
                "cashless exercise") or other disposition of Shares issued
                pursuant to this Notice and that I must consult with my own tax
                advisor regarding how and when such income will be reportable.

__________________________________________      ________________________________
              Signature                                       Date

________________________________INTERNAL USE ONLY_______________________________


<TABLE>
<CAPTION>
<S>     <C>                                 <C>                        <C>
Received [CHECK ONE]:                       | |      By Hand           | |      By Mail Post Marked ________________________________
                                                                                                          DATE OF POST MARK
By_________________________________________________

By_________________________________________________                                                 ________________________________
              AUTHORIZED SIGNATURE                                                                        DATE OF RECEIPT
</TABLE>

<PAGE>

                APPENDIX B TO CONVERSION STOCK OPTION CERTIFICATE
                          BRIDGE STREET FINANCIAL, INC.
                                STOCK OPTION PLAN

                          BENEFICIARY DESIGNATION FORM


GENERAL
INFORMATION     USE THIS FORM TO DESIGNATE THE BENEFICIARY(IES) WHO WILL RECEIVE
                VESTED STOCK OPTIONS OUTSTANDING TO YOU AT THE TIME OF YOUR
                DEATH.


<TABLE>
<CAPTION>
<S>                                                                                   <C>
Name of
Award Recipient ___________________________________________________________________   Social Security Number _______--_____--_______
</TABLE>

BENEFICIARY     COMPLETE SECTIONS A AND B. IF NO PERCENTAGE SHARES ARE
DESIGNATION     SPECIFIED, EACH BENEFICIARY IN THE SAME CLASS (PRIMARY OR
                CONTINGENT) SHALL HAVE AN EQUAL SHARE. IF ANY DESIGNATED
                BENEFICIARY PREDECEASES YOU, THE SHARES OF EACH REMAINING
                BENEFICIARY IN THE SAME CLASS (PRIMARY OR CONTINGENT) SHALL BE
                INCREASED PROPORTIONATELY.

A. PRIMARY BENEFICIARY(IES). I hereby designate the following person as my
primary Beneficiary under the Plan, reserving the right to change or revoke this
designation at any time prior to my death:

<TABLE>
<CAPTION>
                  NAME                                      ADDRESS                      RELATIONSHIP        BIRTHDATE       SHARE
<S>                                             <C>                                   <C>                <C>                <C>
                                                ________________________________
___________________________________________                                           _________________  ________________   _______%
                                                ________________________________

                                                ________________________________
___________________________________________                                           _________________  ________________   _______%
                                                ________________________________

                                                ________________________________
___________________________________________                                           _________________  ________________   _______%
                                                ________________________________
                                                                                                                          Total=100%
</TABLE>

B. CONTINGENT BENEFICIARY(IES). I hereby designate the following person(s) as my
contingent Beneficiary(ies) under the Plan to receive benefits only if all of my
primary Beneficiaries should predecease me, reserving the right to change or
revoke this designation at any time prior to my death:

<TABLE>
<CAPTION>
                  NAME                                      ADDRESS                      RELATIONSHIP        BIRTHDATE       SHARE
<S>                                             <C>                                   <C>                <C>                <C>
                                                ________________________________
___________________________________________                                           _________________  ________________   _______%
                                                ________________________________

                                                ________________________________
___________________________________________                                           _________________  ________________   _______%
                                                ________________________________

                                                ________________________________
___________________________________________                                           _________________  ________________   _______%
                                                ________________________________
                                                                                                                          Total=100%
</TABLE>

<PAGE>



S    H          I understand that this Beneficiary Designation shall be
                effective only if properly completed and received by the
I    E          Corporate Secretary of Bridge Street Financial, Inc. prior to my
                death, and that it is subject to all of the terms and conditions
G    R          of the Plan. I also understand that an effective Beneficiary
                designation revokes my prior designation(s) with respect to all
N    E          outstanding Stock Options.


_____________________________________________   ________________________________
             YOUR SIGNATURE                                 DATE

________________________________INTERNAL USE ONLY_______________________________

<TABLE>
<CAPTION>
This Beneficiary  Designation was received by the Corporate Secretary                               Comments
of Bridge Street Financial, Inc. on the date indicated.
<S>                                                                             <C>





By___________________________________           ________________________________
         AUTHORIZED SIGNATURE                                 DATE
</TABLE>