First Financial Bankshares (FFIN) 10-Q2024 Q3 Quarterly report

Exhibit 32.1

Certification of

Chief Executive Officer

of First Financial Bankshares, Inc.

This certification is provided pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code) and accompanies the quarterly report on Form 10-Q (the “Form 10-Q”) for the quarter ended September 30, 2024 of First Financial Bankshares, Inc. (the “Company”).

I, F. Scott Dueser, the Chairman of the Board, President and Chief Executive Officer of the Company, certify that:

1. the Form 10-Q fully complies with the requirements of section 13(a) or section 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m(a) or 78o(d)); and

2. the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: November 4, 2024

Subscribed and sworn to before me this 4th day of November, 2024.

My commission expires: October 11, 2028