At 1mm thick, it's way too thin for a Bess wrist escutcheon but obviously, it was from some kind of regimentally marked gear. I don't see an "H" on the reverse or a broad arrow. Maybe an "I" but then, there are a lot of random scratches, dings, and marks there. Regardless, it's a nice little piece!
An old friend in Hunterdon County (central NJ, north of Trenton) has a 44th Regt. 1756 Long Land pattern Bess that was supposedly in the family since the 18th century. It was converted to percussion and no doubt saw a lot of use as a fowler along the Delaware but otherwise, completely original and untouched with some very folksy decorative carving in the buttstock. Regimental numbers typically (emphasis on "typically") weren't on the escutcheons but sure enough, there it was along with a company letter and a rack number.