Hezekiah Remington 16 - 50 A , Res. Po, is listed for Coventry, RI, in the 1777 RI Military Census. Also there is William Remington 16 - 50 A (residence Portsmouth), possibly his father; and a Thomas Remington 16 - 50 A.
Hezekiah Remington is on the list of Freemen of Exter, dated 20 Apr 1814.
James N. Arnold's "Family Notes" has his date of birth as 22 May 1757.
I have made an assumption that he was born on Prudence Island; this, in turn, is based on the assumption that his parents are William & Freelove (and Portsmouth land evidence showing this couple on Prudence Island). Hezekiah had two children, named William & Freelove. This is a strong clue. Hezekiah lived in Exeter and North Kingstown, and it is known that William & Freelove bought a house and land there in 1775.