Cain Family IN New York Prior to 1830

I am looking for the Cain family in New York prior to 1830. My best information gives me the name of one Thomas Cain, who supposedly was a Captain in the War of 1812. He was the father of William Cain, who in turn was the father of Glen Cain, who was the father of Harold Eugene Cain, who was my grandad. My name is Jonathan Cain, and my dads name is Harold Joe Cain. I am unsure of how long the cain family has actually been in Denver. Any information anybody has would be really great.