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Your James Simmons, Jr., born 1 Sep 1803 in South Carolina, was married on 4 Jan 1827 in White Co., Tennessee to Margaret Plumlee, daughter of Isaac & Margaret (Bradshaw) Plumlee. James died on 8 June 1870 in Carroll Co., AR.
His parents were James Simmon, Sr. and Statia Roberts. He had a sister named Rachel Simmons, who was born in Feb 1802 in South Carolina and died on 17 Feb 1888. She was married to Joel Plumlee, Sr. Joel and Rachel are both buried in the Blackjack Cemetery in Carroll Co., Arkansas.
That is all the info I have on his parents. Hope this helps!