A Thomas P. Adams (dob and spouse unknown) was another son of Robert ADAMS and wife Mary.He is probably the same man you mention, but I don't have enough information to confirm absolutely. The names of Robert ADAMS parents are unknown.
Here is what I have on this family:
Robert Adams and wife Mary moved from North Carolina to Christian County, Kentucky by 1800 and then to Bedford County, Tennessee around 1810/11 [Marshall County Historical Quarterly, vol 13, p.57]
Descendants of Robert Adams
1 Robert ADAMS b: Bef. 1780 d: Abt. 1829 in Bedford Co, TN +Mary d: Jan 1850 in TN 2 Sarah ADAMS b: 29 Dec 1797 in NC d: 29 Dec 1839 in MO +Samuel W. WOODS b: 04 Nov 1799 in Elbert Co, GA m: 28 July 1818 in Bedford Co, TN d: 23 Sep 1871 in Benton Co, AR 2 James ADAMS b: Bef. 1800 +Polly ELLISON 2 Mary Ann ADAMS b: 1795 in KY d: 28 May 1860 in Springfield, Greene Co, GA +William M. DYSART b: 10 July 1785 in Burke Co, NC m: 1812 in Springfield, Greene County, GA d: 21 Aug 1857 in Springfield, Greene Co, GA 2 Alexander D. ADAMS b: 30 Dec 1802 in Christian Co, KY d: 08 Aug 1866 in Marshall Co, TN +Elizabeth LARUE b: 1803 in Hardin Co, KY d: 1875 2 Eliza Minerva ADAMS b: 22 Feb 1811 in Bedford Co, TN +James HARKNESS m: 10 Nov 1831 in TN 2 Julia ADAMS 2 Mary ADAMS 2 Mary Hannah ADAMS d: 20 Sep 1850 in Bedford Co, TN +Thomas L. DRYDEN b: 29 May 1793 in KY m: 1824 in Bedford Co, TN d: 18 Feb 1873 in Bedford Co, TN 2 Robert N. ADAMS +Eliza Ann LOWE 2 Thomas P. ADAMS