<PAGE>

EXHIBIT 4.4

NEITHER THIS WARRANT NOR THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR QUALIFIED OR REGISTERED
UNDER STATE SECURITIES OR BLUE SKY LAWS.  NEITHER THIS WARRANT NOR SUCH
SECURITIES MAY BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED OR OTHERWISE
TRANSFERRED OR DISPOSED OF EXCEPT IN COMPLIANCE WITH THE SECURITIES ACT OF 1933,
APPLICABLE STATE SECURITIES OR BLUE SKY LAWS AND THE APPLICABLE RULES AND
REGULATIONS THEREUNDER.


                          STOCK PURCHASE "K" WARRANT

No. 3

                 To Purchase 500,000 Shares of Common Stock of

                       THE ASHTON TECHNOLOGY GROUP, INC.


     THIS CERTIFIES that, for value received, TK Holdings, Inc. (the
"Investor"), is entitled, upon the terms and subject to the conditions
hereinafter set forth, at any time on or after June 4, 2000 and on or prior to
June 4, 2002 (the "Termination Date") but not thereafter, to subscribe for and
purchase from THE ASHTON TECHNOLOGY GROUP, INC., a Delaware corporation (the
"Company") five hundred thousand (500,000) shares of Common Stock (the "Warrant
Shares").  The purchase price of one share of Common Stock (the "Exercise
Price") under this Warrant shall be equal to two dollars and fifty cents
($2.50).  The Exercise Price and the number of shares for which the Warrant is
exercisable shall be subject to adjustment as provided herein.  This Warrant is
being issued in connection with that certain Joint Venture Agreement of even
date herewith (the "Agreement") by and among the Investor, TK Holdings, Inc.
In the event of any conflict between the terms of this Warrant and the
Agreement, the Agreement shall control.

          1.  Title of Warrant.  Prior to the expiration hereof and subject to
compliance with applicable laws, this Warrant and all rights hereunder are
transferable, in whole or in part, at the office or agency of the Company by the
holder hereof in person or by duly authorized attorney, upon surrender of this
Warrant together with the Assignment Form annexed hereto properly endorsed.

          2.  Authorization of Shares.  The Company covenants that all shares of
Common Stock which may be issued upon the exercise of rights represented by this
Warrant will, upon exercise of the rights represented by this Warrant, be duly
authorized, validly issued, fully paid and nonassessable and free from all
taxes, liens and charges in respect of the issue thereof (other than taxes in
respect of any transfer occurring contemporaneously with such issue).
<PAGE>

          3.  Vesting of Shares Underlying Warrant.  The right to purchase the
Warrant Shares shall vest in quarterly installments of one hunderd and twenty-
five thousand (125,000) shares beginning on the first anniversary of the Closing
Date (as defined in the Agreement) and on the last business day of each complete
calendar quarter thereafter.

          4.  Exercise of Warrant.  Exercise of the purchase rights represented
by this Warrant may be made at any time or times, in whole, before the close of
business on the Termination Date, or such earlier date on which this Warrant may
terminate as provided in paragraph 13 below, by the surrender of this Warrant
and the Subscription Form annexed hereto duly executed, at the office of the
Company (or such other office or agency of the Company as it may designate by
notice in writing to the registered holder hereof at the address of such holder
appearing on the books of the Company) and upon payment of the Exercise Price of
the shares thereby purchased; whereupon the holder of this Warrant shall be
entitled to receive a certificate for the number of shares of Common Stock so
purchased.  Certificates for shares purchased hereunder shall be delivered to
the holder hereof within five business days after the date on which this Warrant
shall have been exercised as aforesaid.  Payment of the Exercise Price of the
shares may be by certified check or cashier's check or by wire transfer to an
account designated by the Company in an amount equal to the Exercise Price
multiplied by the number of shares being purchased.

          5.  Mandatory Exercise.  At the written demand of the Company, at the
Company's sole discretion, the Investor shall exercise any remaining portion of
the Warrant on the first business day following the twentieth (20th) consecutive
business day on which the closing stock price of the Common Stock of the Company
on the Nasdaq Small Cap Market, or each other securities market on which such
shares are listed for trading, shall exceed $15 per share.  Any unvested portion
of the Warrant shall vest immediately upon such written demand by the Company.
If the Investor shall fail to exercise this Warrant within thirty (30) days of
the demand made by the Company pursuant to this Section 5, this Warrant shall
terminate.

          6.  No Fractional Shares or Scrip.  No fractional shares or scrip
representing fractional shares shall be issued upon the exercise of this
Warrant.

          7.  Charges, Taxes and Expenses.  Issuance of certificates for shares
of Common Stock upon the exercise of this Warrant shall be made without charge
to the holder hereof for any issue or transfer tax or other incidental expense
in respect of the issuance of such certificate, all of which taxes and expenses
shall be paid by the Company, and such certificates shall be issued in the name
of the holder of this Warrant or in such name or names as may be directed by the
holder of this Warrant; provided, however, that in the event certificates for
shares of Common Stock are to be issued in a name other than the name of the
holder of this Warrant, this Warrant when surrendered for exercise shall be
accompanied by the Assignment Form attached hereto duly executed by the holder
hereof; and provided further, that upon any transfer involved in the issuance or
delivery of any certificates for shares of Common Stock, the Company may
require, as a condition thereto, the payment of a sum sufficient to reimburse it
for any transfer tax incidental thereto.
<PAGE>

          8.  Closing of Books.  The Company will at no time close its
shareholder books or records in any manner which interferes with the timely
exercise of this Warrant.

          9.  No Rights as Shareholder until Exercise.  This Warrant does not
entitle the holder hereof to any voting rights or other rights as a shareholder
of the Company prior to the exercise thereof.  If, however, at the time of the
surrender of this Warrant and purchase the holder hereof shall be entitled to
exercise this Warrant, the shares so purchased shall be and be deemed to be
issued to such holder as the record owner of such shares as of the close of
business on the date on which this Warrant shall have been exercised.

          10.  Assignment and Transfer of Warrant.  This Warrant may be assigned
by the surrender of this Warrant and the Assignment Form annexed hereto duly
executed at the office of the Company (or such other office or agency of the
Company as it may designate by notice in writing to the registered holder hereof
at the address of such holder appearing on the books of the Company); provided,
however, that this Warrant may not be resold or otherwise transferred except (i)
in a transaction registered under the Securities Act of 1933, as amended, or
(ii) in a transaction pursuant to an exemption, if available, from such
registration and whereby, if requested by the Company, an opinion of counsel
reasonably satisfactory to the Company is obtained by the holder of this Warrant
to the effect that the transaction is so exempt.

          11.  Loss, Theft, Destruction or Mutilation of Warrant.  The Company
represents and warrants that upon receipt by the Company of evidence reasonably
satisfactory to it of the loss, theft, destruction or mutilation of any Warrant
or stock certificate, and in case of loss, theft or destruction, of indemnity or
security reasonably satisfactory to it, and upon reimbursement to the Company of
all reasonable expenses incidental thereto, and upon surrender and cancellation
of such Warrant or stock certificate, if mutilated, the Company will make and
deliver a new Warrant or stock certificate of like tenor and dated as of such
cancellation, in lieu of this Warrant or stock certificate.

          12.  Saturdays, Sundays, Holidays, etc.  If the last or appointed day
for the taking of any action or the expiration of any right required or granted
herein shall be a Saturday, Sunday or a legal holiday, then such action may be
taken or such right may be exercised on the next succeeding day not a legal
holiday.

          13.  Effect of Certain Events.

               (a) If at any time the Company proposes (i) to sell or otherwise
convey all or substantially all of its assets or (ii) to effect a transaction
(by merger or otherwise) in which more than 50% of the voting power of the
Company is disposed of (collectively, a "Sale or Merger Transaction"), in which
the consideration to be received by the Company or its shareholders consists
solely of cash, the Company shall give the holder of this Warrant thirty (30)
days' notice of the proposed effective date of the transaction specifying that
the Warrant shall terminate if the Warrant has not been exercised by the
effective date of the transaction.

                                       3
<PAGE>

               (b) In case the Company shall at any time effect a Sale or Merger
Transaction in which the consideration to be received by the Company or its
shareholders consists in part of consideration other than cash, the holder of
this Warrant shall have the right thereafter to purchase, by exercise of this
Warrant and payment of the aggregate Exercise Price in effect immediately prior
to such action, the kind and amount of shares and other securities and property
which it would have owned or have been entitled to receive after the happening
of such transaction had this Warrant been exercised immediately prior thereto.

               (c) "Piggy-Back" Registration. The holder of this Warrant shall
have the right to include all of the shares of Common Stock underlying this
Warrant (the "Registrable Securities") as part of any registration of securities
filed by the Company (other than in connection with a transaction contemplated
by Rule 145(a) promulgated under the Act or pursuant to Form S-8) and must be
notified in writing of such filing. Holder shall have five (5) business days to
notify the Company in writing as to whether the Company is to include holder or
not include holder as part of the registration; provided, however, that if any
registration pursuant to this Section shall be underwritten, in whole or in
part, the Company may require that the Registrable Securities requested for
inclusion pursuant to this paragraph 13(c) be included in the underwriting on
the same terms and conditions as the securities otherwise being sold through the
underwriters.  If in the good faith judgment of the underwriter evidenced in
writing of such offering only a limited number of Registrable Securities should
be included in such offering, or no such shares should be included, the holder,
and all other selling stockholders, shall be limited to registering such
proportion of their respective shares as shall equal the proportion that the
number of shares of selling stockholders permitted to be registered by the
underwriter in such offering bears to the total number of all shares then held
by all selling stockholders desiring to participate in such offering.  Those
Registrable Securities which are excluded from an underwritten offering pursuant
to the foregoing provisions of this paragraph 13(c) (and all other Registrable
Securities held by the selling stockholders) shall be withheld from the market
by the holders thereof for a period, not to exceed one hundred eighty (180)
days, which the underwriter may reasonably determine is necessary in order to
effect such underwritten offering.

          14.  Adjustments of Exercise Price and Number of Warrant Shares.  The
number and kind of securities purchasable upon the exercise of this Warrant and
the Exercise Price shall be subject to adjustment from time to time in case the
Company shall (i) declare or pay a dividend in shares of Common Stock or make a
distribution in shares of Common Stock to holders of its outstanding Common
Stock, (ii) subdivide its outstanding shares of Common Stock, (iii) combine its
outstanding shares of Common Stock into a smaller number of shares of Common
Stock or (iv) issue any shares of its capital stock in a reclassification of the
Common Stock, the number of Warrant Shares purchasable upon exercise of this
Warrant immediately prior thereto shall be adjusted so that the holder of this
Warrant shall be entitled to receive the kind and number of Warrant Shares or
other securities of the Company which such holders would have owned or have been
entitled to receive had such Warrant been exercised in advance thereof.  An
adjustment made pursuant to this paragraph shall become effective immediately
after the effective date of such event retroactive to the record date, if any,
for such event.

                                       4
<PAGE>

          15.  Voluntary Adjustment by the Company.  The Company may at its
option, at any time during the term of this Warrant, reduce the then current
Exercise Price to any amount and for any period of time deemed appropriate by
the Board of Directors of the Company.

          16.  Notice of Adjustment.  Whenever the number of Warrant shares or
number or kind of securities or other property purchasable upon the exercise of
this Warrant or the Exercise Price is adjusted, as herein provided, the Company
shall promptly mail by registered or certified mail, return receipt requested,
to the holder of this Warrant notice of such adjustment or adjustments setting
forth the number of Warrant Shares (and other securities or property)
purchasable upon the exercise of this Warrant and the Exercise Price of such
Warrant Shares after such adjustment, setting forth a brief statement of the
facts requiring such adjustment and setting forth computation by which such
adjustment was made.  Such notice, in absence of manifest error, shall be
conclusive evidence of the correctness of such adjustment.

          17.  Authorized Shares.  The Company covenants that during the period
the Warrant is outstanding, it will reserve from its authorized and unissued
Common Stock a sufficient number of shares to provide for the issuance of Common
Stock upon the exercise of any purchase rights under this Warrant.  The Company
further covenants that its issuance of this Warrant shall constitute full
authority to its officers who are charged with the duty of executing stock
certificates to execute and issue the necessary certificates for shares of the
Company's Common Stock upon the exercise of the purchase rights under this
Warrant.  The Company will take all such reasonable action as may be necessary
to assure that such shares of Common Stock may be issued as provided herein
without violation of any applicable law or regulation, or of any requirements of
the NASDAQ Small Cap Stock Market or any domestic securities exchange upon which
the Common Stock may be listed for trading.

          18.  Miscellaneous.

               (a) Issue Date; Jurisdiction. The provisions of this Warrant
shall be construed and shall be given effect in all respects as if it had been
issued and delivered by the Company on the date hereof. This Warrant shall be
binding upon any successors or assigns of the Company. This Warrant shall
constitute a contract under the laws and jurisdictions of New York and for all
purposes shall be construed in accordance with and governed by the laws of said
state without regard to its conflict of law, principles or rules and be subject
to the arbitration provisions as set forth in the Agreement.

               (b) Restrictions.  The holder hereof acknowledges that the Common
Stock acquired upon the exercise of this Warrant, if not registered, may have
restrictions upon its resale imposed by state and federal securities laws.

               (c) Modification and Waiver. This Warrant and any provisions
hereof may be changed, waived, discharged or terminated only by an instrument in
writing signed by the party against which enforcement of the same is sought.

                                       5
<PAGE>

               (d) Notices.  Any notice, request or other document required or
permitted to be given or delivered to the holders hereof of the Company shall be
delivered or shall be sent by certified or registered mail, postage prepaid, to
each such holder at its address as shown on the books of the Company or to the
Company at the address set forth in the Agreement.

          IN WITNESS WHEREOF, the Company has caused this Warrant to be executed
by its officers thereunto duly authorized.


Dated: June 4, 1999

                              THE ASHTON TECHNOLOGY GROUP, INC.


                              By: /s/ Arthur J. Bacci
                                  _________________________________________
                                  Name:  Arthur J. Bacci
                                  Title:  President

                                       6
<PAGE>

                              NOTICE OF EXERCISE

To:  THE ASHTON TECHNOLOGY GROUP, INC.

(1) The undersigned hereby elects to purchase ________ shares of Common Stock of
THE ASHTON TECHNOLOGY GROUP, INC. pursuant to the terms of the attached Warrant,
and tenders herewith payment of the purchase price in full, together with all
applicable transfer taxes, if any.

(2) Please issue a certificate or certificates representing said shares of
Common Stock in the name of the undersigned or in such other name as is
specified below:

                    _______________________________(Name)
                    _______________________________(Address)____________________
                    ___________


Dated:
______________________________Signature







                                       1
<PAGE>

                                ASSIGNMENT FORM

                   (To assign the foregoing warrant, execute
                  this form and supply required information.
                Do not use this form to exercise the warrant.)



          FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced
thereby are hereby assigned to

_______________________________________________ whose address is

_______________________________________________________________.



_______________________________________________________________

                                    Dated:  ___________________,


               Holder's Signature:  ___________________________

               Holder's Address:    ___________________________

                                    ___________________________



Signature Guaranteed:  ____________________________________



NOTE:  The signature to this Assignment Form must correspond with the name as it
appears on the face of the Warrant, without alteration or enlargement or any
change whatsoever, and must be guaranteed by a bank or trust company.  Officers
of corporations and those acting in an fiduciary or other representative
capacity should file proper evidence of authority to assign the foregoing
Warrant.

                                       2