Moses Johnson, III - Who are the parents of Moses Johnson born 1777 in Cheshire City, New Hampshire?

Moses Johnson was attached to Moses Johnson II and Elizabeth Underwood but the problem is that they have a son, Moses b. 1755, who apparently grew to adulthood and married.

I have been looking and can't find good sources yet for this Moses Johnson who may be Moses C. Johnson. It's not sure that he's connected to the Southborough, Massachusetts family.