I'm stuck and need help again!

Is there anyone here that can tell me what Regiments were in and around New York in the 1770s until they left in 1783?
Also what Royal Navy ships would have been there?
I am having a major problem trying to find out if my ancestor was in the Royal Navy or an Army Regiment as I now have 4 conflicting reports from various family documentation.
All reports agree he was Lieutenant John Thompson, but one states he was in the RN, another in the 69th Foot, yet another the 95th foot and a last report says 96th (which I couldn't find to exist at all).
Apart from family tales the only actual proof I have that he was really in New York is a (belated) birth registration (from English parish records) for a son. John swears by oath in 1799, that his son was born Nov. 1779 "at Brooklyne on Long-Island in the Province of New York".
Any help would be greatly appreciated.
Karen