There is some doubt if he is son of Thomas Payton (~1755-~1835). Thomas also had a son named John by his 3rd wife.
In 1810 he may have been with his father in Mason Co., Kentucky. Thomas Payton in 1810 census has one male age 16 to 25. This could be either John or Lewis, son by 2nd wife of Thomas Payton. Could find only one John Payton (Peyton) in 1810 census in Kentucky (Bourbon County). This could not be this John Payton as he has a large family with oldest male over age 25. There is a James Peyton in Washington County with one male age 16 to 25 and one female age 16 to 25. This could be John. He is next to a Lewis Peyton.
In 1820 census there is a John Payton in Mason Co., Kentucky. This could be him with his father (male age over 44), although the next oldest male is a bit young for birth year of 1791.
In 1830 census there is a John Payton in Mason Co., Kentucky with two males age 5 to 10, two females age under 5, one female age 5 to 10, one female age 10 to 15, one female age 15 to 20, and one female age 20 to 30 (presumably his younger 2nd wife and children from 1st wife).
In 1840 census there is a John Payton in Mason Co., Kentucky with one male under age 5, one male age 15 to 19, one male age 20 to 29, two females age 5 to 9, one female age 10 to 14, one female age 15 to 19, one female age 20 to 29, and one female age 30 to 39 (presumably his younger 2nd wife and children from 1st wife).