I have a Nathaniel White born ca 1790's in N.C., he md Mary S. Allen, the daughter of John and Nancy Allen of Bedford Co, Tenn. This Nathaniel is a brother-in-law to my Abigail Allen Epps.
Known children were: Thomas born ca 1828, Mary, Nancy, Margaret, Jane and Milton.
The above Nancy md Thomas Moore and they are found in 1850 Giles Co, Tenn.
Margaret md George Ellis and in 1850 in Tishomingo Co, Miss and were in Prentiss Co, Miss 1880 and 70.
Abigail md Peter Irby Epps and she died early, but family lived Tishomingo and Alcorn Co, Miss and then to McNairy Co, Tenn.
The John Allen family lived around the Elk Ridge on the headwaters of Sugar Creek and Cane Creek.
Just thought there may be some connection to your White's.
Wish I could help with the DNA that you need,but not my direct line.