My records do not show a son of Bartholomew named Bartlett. I do know that Bartholomew and Bartlett were both used as Bartholomew's (born abt 1761-5) name, because I have a copy of the bond between James Nevils and Nancy Brooks "spinster daughter of Bartlett Brooks" as stated on the bond.
I have a lot of documentation from Claiborne Co. Tenn concerning Bart, Hezehiah, Gideon, Armstead and Nancy, and their decendents, but none as to him having a son Bartlett. I know Littleton Brooks came to Claiborne Co. and had a son Thomas Brooks. Do you have any kind of documentation that might show Littletons relationship to Bartholomew Brooks? Littleton may have been a younger son of Bartholomew as Littleton Brooks was born 1800 to 1810 accd to the 1840 CC Census with three sons and three daughters and a wife age 20 to 30. He could have been another son of Bartholomew and Nancy Brooks? Littleton was indexed as having a will made in Claibonre Co Tenn, on Book A 1837-1846 wills, page 14.
Let me know if you have any more records that I have missed to prove Littleton's paternaty.