Sorry, but John Quincy Adams and J.Q. Adams were indeed twin sons of Amos Adams and Judith Taunton, according to both strong family tradition and a direct descendant who has Amos' estate papers. According to all records and family tradition, J.Q.'s name was nothing more than that -- just the two initials. He and John Quincy were definitely separate individuals, with separate census entries (and separate families) in Taylor Co., GA in 1860.
The complete list of children for Amos Adams and Judith Taunton is: 1) Ezekiel Amos Adams (c1822-1854) 2) J.Q. Adams (c1827-?) - twin to John Quincy Adams 3) John Quincy Adams (c1827-?) - twin to J.Q. Adams 4) Sampson Adams (c1829-?) 5) Catherine Adams (c1830-?) 6) Miranda Adams (c1835-?)
Amos Adams married Telitha Whittington on 4 May 1837, and had the following children by her: 1) James E. Adams (1838-?) 2) Amos Allen Adams (c1839-?) 3) Elizabeth Adams (1847-?) - twin to Joseph Andrew Jackson Adams 4) Joseph Andrew Jackson Adams (1847-?) - twin to Elizabeth Adams 5) Perry Z.T. Adams (c1849-?)