He may be the Sylvester Gardiner Hazard mentioned as a son in the will of Robert Hazard, physician, of South Kingstown, RI. This will was dated 8 FEb 1771.
[S013125] Dorothy Higson White, compiler, Descendants of Roger Williams, Book III, Sayles Line, (East Greenwich, RI: Roger Williams Family Association, 2002), 286.