Here's a probability, FamilySearch is pretty good at this. I input his name and a span of years for his birth. This is the result.
Aaron Bates, b 6 Nov 1757, Durham Twp, Middlesex Co. Conn. Parents: Stephen and Mindwell Bates.
Connecticut, Births and Christenings, 1649-1906," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/F741-W9Q : accessed 26 Sep 2012), Aaron Bates, 06 Nov 1757; citing reference , FHL microfilm unknown.