Exhibit 4.1


 


SPECIMEN UNIT CERTIFICATE


 


NUMBER UNITS U-[__]


 


Alpha Healthcare Acquisition Corp. III


 


SEE REVERSE FOR


CERTAIN


	DEFINITIONS	CUSIP[___]


 


Alpha
Healthcare Acquisition Corp. III


UNITS CONSISTING OF ONE SHARE
OF CLASS A COMMON STOCK AND ONE-FOURTH

OF ONE REDEEMABLE WARRANT, EACH WHOLE WARRANT ENTITLING THE

HOLDER TO PURCHASE ONE SHARE OF CLASS A COMMON STOCK


 


THIS CERTIFIES THAT          is the owner of          Units.


 


Each Unit
(“Unit”) consists of one share of Class A common stock, par value $0.0001 per share
(“Common Stock”), of Alpha Healthcare Acquisition Corp. III, a Delaware corporation (the
“Company”), and one-fourth of one redeemable warrant (the “Warrant”). Each whole
Warrant entitles the holder to purchase one share of Common Stock for $11.50 per share (subject to adjustment). Only whole
Warrants are exercisable. Each whole Warrant will become exercisable thirty (30) days after the Company’s completion of
a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or other similar business combination
with one or more businesses (each a “Business Combination”), and will expire unless exercised
before 5:00 p.m., New York City Time, on the date that is five (5) years after the date on which the Company completes its
initial Business Combination, or earlier upon redemption or liquidation (the “Expiration Date”).
The Common Stock and Warrants comprising the Units represented by this certificate are not transferable separately prior
to          , 2021, unless BofA Securities, Inc. and PJT Partners LP elect
to allow separate trading earlier, subject to the Company’s filing of a Current Report on Form 8-K with the Securities
and Exchange Commission containing an audited balance sheet reflecting the Company’s receipt of the gross proceeds of
the Company’s initial public offering and issuing a press release announcing when separate trading will begin. No
fractional Warrants will be issued upon separation of the Units. The terms of the Warrants are governed by a Warrant
Agreement, dated as of           , 2021, between the Company and
Continental Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms and provisions contained
therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies of the
Warrant Agreement are on file at the office of the Warrant Agent at 1 State Street, 30th Floor, New York, New York 10004, and
are available to any Warrant holder on written request and without cost.


 


This certificate is
not valid unless countersigned by the Transfer Agent and registered by the Registrar of the Company.


 


This certificate shall
be governed by and construed in accordance with the internal laws of the State of Delaware.


 


Witness the facsimile
signature of a duly authorized signatory of the Company.


 


	 	 	 
	Authorized Signatory	 	Transfer Agent


 






     


     


    

 


Alpha Healthcare Acquisition Corp. III


 


The Company will furnish
without charge to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating,
optional or other special rights of each class of equity or series thereof of the Company and the qualifications, limitations,
or restrictions of such preferences and/or rights.


 


The following abbreviations,
when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according
to applicable laws or regulations:


 





	TEN COM	—	as tenants in common	 	UNIF GIFT MIN ACT	—	 	Custodian	 
	 	 	 	 	 	 	(Cust)	 	(Minor)
	TEN ENT	—	as tenants by the entireties	 	 	 		 	
	 	 	 	 	 	 	 	 	 
	JT TEN	—	as joint tenants with right of survivorship
    and not as tenants in common	 	 	under
    Uniform Gifts to Minors Act
	 	 	 	 	(State)


  


 


Additional abbreviations may also be used
though not in the above list.


 






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For value received,                    hereby sells, assigns and transfers unto


 


(PLEASE INSERT SOCIAL SECURITY OR OTHER
IDENTIFYING NUMBER OF ASSIGNEE)


 


(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS,
INCLUDING ZIP CODE, OF ASSIGNEE)


 


Units represented by the within Certificate,
and does hereby irrevocably constitute and appoint Attorney to transfer the said Units on the books of the within named Company
with full power of substitution in the premises.


 


	Dated	 	 



 


	 	 
	 	 
	 	Notice: The signature to this assignment must correspond with the name as written upon the face of the certificate in every particular, without alteration or enlargement or any change whatever.


 


Signature(s) Guaranteed:


 


	 	 
	THE SIGNATURE(S) MUST BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15 UNDER THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED (OR ANY SUCCESSOR RULE)).	 


 


As more fully described
in, and subject to the terms and conditions described in, the Company’s final prospectus for its initial public offering
dated           , 2021 (the “Final Prospectus”), the holder(s) of this certificate shall be entitled to receive a pro rata portion
of certain funds held in the trust account established in connection with the Company’s initial public offering only in the
event that (i) the Company redeems the shares of Common Stock sold in the Company’s initial public offering and liquidates
because it does not consummate an initial business combination by the date set forth (the “Last Date”) in the Company’s
Amended and Restated Certificate of Incorporation, as the same may be amended from time to time (the “Charter”), (ii)
the Company redeems the shares of Common Stock sold in its initial public offering properly submitted in connection with a stockholder
vote to amend the Charter to modify the substance or timing of the Company’s obligation to provide redemption rights as described
in the Final Prospectus or with respect to any other material provisions relating to stockholders’ rights or pre-initial
business combination activity, or (iii) if the holder(s) seek(s) to redeem for cash his, her or its respective shares of Common
Stock in connection with a tender offer (or proxy solicitation, solely in the event the Company seeks stockholder approval of the
proposed initial business combination) setting forth the details of a proposed initial business combination. In no other circumstances
shall the holder(s) have any right or interest of any kind in or to the trust account.


 




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