Joseph LeCompte (1792-1852) son of Charles LeCompte (1749-1824) and Elizabeth Coons who married 1779. Joseph had only three children that I know of, Charles, Mary and Elizabeth, but they were all born around 1821. Perhaps there was a Joseph, Jr.? Certainly I know that Charles and Mary both had sons named Joseph, but they were born later than 1821.
Isaac LeCompte (1788-1826) also son of Charles and Elizabeth Coons, who definitely had a son named Joseph, who was probably born around 1821. I know nothing about this Joseph, other than he was probably named for his uncle and the timing is right for your Joseph.
there are a couple of Joseph LeComptes that descend from Moses LeCompte (1664-1718) and Mary Skinner (1667-unk) who married in 1687, who might also connect to your Joseph.