PA - papers applied -- or something to that effect. He has started the process of naturalization. That means some court or the national government has copies of the papers he filed!
Looking for naturalization papers is a unique study. There are websites and books about it. I'm not well versed or experienced at it so cannot advise further.
You could also look for the passenger manifest at his port of arrival... New York? Boston? Quebec? By that year the American officials were collecting a good amount of information about each person arriving.