Parker's mother was Sarah Work(e) who he married in 1817.He married Janette League in 1839.Parker was born in Nashville, Davidson County Tn Oct 24 1819.His sister Matilida Esther was born May 29, 1818.These dates come after the marriage date in the Tennessee marriage records for James and Sarah Work.Not Janette League.I do not think that he had any children with Janette.The last child of James that I have was born in 1836 which was before James' marriage to Janette.
Parker's grandfather as far as I can determine is not known.There are several "guesses" but I have not seen any records to support the information.
Parker had a brother Henry born Jan 12, 1825.Perhaps he was named after Henry Levi who began in NC and moved to Tenn as Parker's father James Allison did.
But James also had a son named Alexander born in 1823.And of course there is your grandfather, Parker Milton who is the first son.I do not know who he is named after.
My grandfather was Robert Levy son of James Allsion Levy, jr.His grandfather was James Allison Levy, Sr.