EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. 1350

(SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002)

In connection with the Quarterly Report of Alpha Healthcare Acquisition Corp. III (the “Company”) on Form 10-Q for the quarter ended June 30, 2022, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Rajiv Shukla, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

• the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

• the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: August 10, 2022	By:	/s/ Rajiv Shukla
	Rajiv Shukla
	Chief Executive Officer
	(Principal Executive Officer)