Ada - I know who you are asking about, the mother of Minerva Turney.
There seems to have been 3 groups of Adams in Smith Co TN same time as the Turneys....one I think came out of Kentucky and they did not live near the Turneys....there was a Jacob Adams in 1806 Hawkins Co TN near the Turneys....and the group of Adams out of Patrick Co Virginia.
As far as Searcy Co Arkansas in 1850 look at James Adams in Tomahawk Township, age 50 born TN.If he was born in Tennessee ca 1800 then he is not from the Patrick Co VA Adams group since they arrived in TN from VA after 1800. This James Adams in 1850 Searcy Co AR was husband of Mary Turney (sister of the George Turney you are asking about)....so I wonder if you should look at him.Since Mary Turney Adams and George Turney were sister and brother - perhaps there is a connection between James Adams born ca 1800 TN and Sarah Adams Turney born 1824 TN.
I found James Adams age 50 TN - wife Mary Turney - at house #133 Tomahawk Twp., Searcy Co AR 1850 house #112 was Robert Adams age 56 KY, wife Cinthia age 51 KY house #117 Joseph Adams age 23 AR, wife Elvira Jane 22 TN.
This Mary Adams Turney - husband James....in 1850 besides their children in household, there is Olive Jane Adams age 18 - this would put her born ca 1832 - is she a child of James Adams from a previous marriage?The next child is age 9 so that is quite a gap.
As far as Tennessee goes: William A. Turney born 1814 Smith Co TN, s/o George Turney and Catherine Barger - married Susan Jane Adams around 1841.This Susan Jane Adams was born 30 April 1821 in TN, died 1890 - William A. Turney died 1857.Susan Jane Adams is supposed to be the daughter of Abraham Adams.
Abraham Adams was born ca 1788 VA and is from the Patrick Co VA group.Besides Susan Jane born 1821, I have Hannah Leann Adams, and Jacob Adams born ca 1815 TN (wife Lucretia) and this Jacob Adams in the 1860 Dekalb Co TN census has living with him Abraham Adams age 72 born VA.
I am interested in this Abraham Adams since I think he might be a brother to my Hannah Adams Turney born 1796 Va the wife of Peter Turney who died 1842 Van Buren Co Arkansas.
Abraham Adams born ca 1788 VA - think his father was Jacob Adams Jr of Pat. Co VA.....this Jacob Jr sister Mary Adams first married a Cooper and then Richard Hancock. Richard Hancock line comes in to the Turneys....also in 1834 before moving to Arkansas, my Peter Turney (wife Hannah Adams) sold his land on Clear Forks to an Alfred Hancock.
Our Henry Turney (d 1843 Dekalb Co TN) in Feb 1816 sold 84 acres of his Clear Fork land to Jacob Adams proven by oath of Abraham Adams.My Hannah Adams married Peter Turney (son of Henry) in 1812 Smith Co TN.