There is a service record for a Jonathan Bayles as well as muster rolls for him at Footnote.com. Jonathan Bayles served in the 5th NY, Capt. Henry Godwin's Co. of Foot in the Regt. commanded by Col. Lewis Duboys. This was also called Capt. Henry Godwin's Co. in the Battalion of NY Forces commanded by Caol. Lewis Duboys.

Jonathan Bayles enlisted May 6, 1777 and was discharged March 7, 1780. He was mustered as a Sgt. in Oct. 1777 and was discharged at that rank. As Sgt., he kept the muster rolls and his signature appears on them. In the service record (29 images at Footnote) the surname is spelled BAILEY on 3 or 3 of the cards.

I did not find a pension file for him. A Jonathan Bayles made a statement for Nicholas Storms that he (Jonathan) had been present at the wedding of Nicholas and his wife Nancy who was sister to Jonathan Bayles, son of Jonathan.