Louise, I'm descended from the William Peyton who was born in North Carolina and died in Bourbon, KY. My records show him as being born in 1718, not 1715, so there is a slight discrepancy there.
If memory serves, there is a Charles Payton on the early Kentucky censuses with William. My guess would be that William and Charles are cousins. I have no way of being sure, but family members did tend to travel together.
I have had similar problems tracking my branch. They came to Kentucky when it was just being settled and seem to have left very little public record of themselves in their early days there.
Do you know anything more about your Charles? He is in the right age group to be a cousin to my William.