I have seen many genealogical instances of UK immigrants to the USA, who never had nor ever used a middle name in England yet suddenly sprouted one in the form of a middle initial in the USA. Often found to be the maiden name of a mother.
I saw the John Jones you mentioned in the place you mentioned in PA, as then discuused above.. wanted to clarify that.
As research Rootschat friends, we're concerned to establish you are tracing the right people. Could I ask, who is the descendant of John and Mary - a child or grandchild perhaps, of whom you are 110% percent sure? Name, birth, married, locations?
Cheers
AMBLY