Dear Ms. Herzog,
Thank you for posting your request on History Hub,
We are unfamiliar with the term “Adjutant General Certificate” in relation to the Revolutionary War records in the custody of the National Archives. Please respond with more details about the nature of the document you are seeking and the name of the soldier you are researching and will gladly provide specific advice on this matter. If you have already located a document pertaining to your research, you may insert an image of it in your reply.
See NARA’s The American Revolution: Research our Records web page for a listing of records commonly used to document individual service in the Revolutionary War. For more information about these records, please post a follow-up request here on History Hub or email the National Archives at Washington, DC - Textual Reference (RDT1) and Archives1reference@nara.gov
The New Jersey State Archives, New Jersey State Library, New Jersey Historical Society, and the New Jersey State Museum may have records relating to the soldiers who fought in the American Revolution from New Jersey.
We hope this is helpful.