|The NY State Department provides an excerpt of NY notary laws at|
But if you follow the logical links from their website at https://dos.ny.gov you can't find the law summary, so I will regard that summary as abandoned.
The relevant NY law can be found at
It says in part "Statement as to authority of notaries public. In exercising powers pursuant to this article, a notary public, in addition to the venue of the act and signature of such notary public, shall print, typewrite, stamp, or affix by electronic means where performing an electronic notarial act in conformity with section one hundred thirty-five-c of the executive law, beneath their signature in black ink, the notary public's name, the words "Notary Public State of New York," the name of the county in which such notary public originally qualified, and the expiration date of such notary public's commission and, in addition, wherever required, a notary public shall also include the name of any county in which such notary public's certificate of official character is filed, using the words "Certificate filed ........... County."
It goes on to provide other details, including that if a notary filed a certificate of official character in one of the counties that make up New York City the number assigned by the county must be written in the certificate in black ink. I think the use of "black ink" in the two places in the law mean it applies to the printed information about the notary, and not the signature itself.