Carothers in TN

Searching for Carothers connection: William Robert Ball (1917 CO -2001 TX), son of Annie Carothers Ball (17 May 1896 TN – 18 Dec 1974 TX), daughter of Thomas Kennedy Carothers (10 Mar 1856 TN – 9 August 1906 OK) and Tommie English Carothers ( 9 Sept 1858 TN – 11 Nov 1922 OK) , son of Hugh C. Carothers (b 1809 TN – d, probably after 1900) and Jane Wells Carothers (b 1815 VA – d unkn TN?). To this point, verifiable sources. However, many on-line researchers have Hugh C. as the son of Hugh Carothers (1766-1832) and Martha Irvin Carothers (married 1796), who is the son of Robert B. Carothers (1750-1812) and Margaret Scott (married 1760) who is the son of Hugh Carothers (1747 -1782) and Sarah Purviance. However, the birth dates obviously show that Robert B. Carothers could not be the son of Hugh Carothers/Purviance. The Carothers lines are obviously long and complicated due to repeated first names. Any clues fellow Carothers researchers or substantiated resources to suggest? Thank you!!

My Caruthers were in Cannon Co., Tn. They came from Lincoln, N.C., and Mecklenberg Co., N.C. into Rutherford Co., Tn., then into Cannon County, Tn. Then some of them came to Arkansas. My line was Edmond Caruthers, his son Maxwell, Maxwell's dau. Amanda, Amanda's son Andrew Franklin Jackson, Amanda and Andrew Franklin's dau. Clementine Jackson Tomlinson (who was my Grandmother.
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Betty McCollum