Thanks Dianne for the reply!
I'll respond directly to you with more details, but the long and short of it is this - I have no record or evidence of my Jesse Cain/Cane being in Kentucky - only Pennsylvania and Ohio. And as for his son Jesse Smith Cain, it is a Pennsylvania birth, Ohio residence, Civil War service, and Indiana residence until his death.
There is a Cain line with a number of Jesse's in it, but I've been unable to make a positive connection to it. If there is a connection between us, it may go back many more generations than what I have evidence for.
I'm also participating in the Cain DNA project as another way to help narrow down the possible Cain lines for me.