It looks like maybe not a papaya, now that I've found a larger fruit on it. (I had wondered about the fruit size. If it is papaya, I doubt our weather would let us get a fruit before the freezes set in.) The leaves are very papaya like and are identical in shape to the ones in that article I posted.
Anyway, the thing that makes me doubt the the papaya qualities of my volunteer despite the leaf shape (along with the really weird location) is
a fruit that looks just like this. Fig maybe?