Old Joe Clark goes back a long ways (pub. 1842, "Nursery Rhymes," Halliwell) and probably older.
'Joe Clark' cannot be referred or traced to anyone, no connections can be made.
I prefer this one:
Old Joe Clark is a preacher,
He preached all over the plain,
The highest text he ever took
Was high, low, jack and the game!

(Randolph, Ozark Folk-Songs, vol. 3, p. 124. Many verses, everyone has contributed over the years).

See the threads, esp. 25394 and 48624.

Old Joe Clark 25394
Old Joe Clark 48624