According to the index of Clinton Co NY naturalization record, Benjamin Marriott filed his declaration of intention on 17 Dec 1831 and was naturalized 7 Dec 1934.
It will likely be necessary to know what county your ancestor was living in when he naturalized.
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Dear Ms. Griffen,
Thank you for posting your request on History Hub!
In most cases, the National Archives will not have a copy of his certificate of citizenship. Two copies of the certificate were created – one given to the petitioner as proof of citizenship, and one forwarded to the Immigration and Naturalization Service (INS). All INS records are now overseen by the US Citizenship and Immigration Services (USCIS). We suggest that you request an index search through the USCIS to identify any naturalization records for your grandfather. You may order any records through the same site.
We hope this is helpful. Best of luck with your family research!