Can’t find Cherokee connection in ancestor

Hello!

I am supposedly descended from a Chief Nathan “Cheese squire” Kirkland (b. 1750 in Graham Co. NC) on my great-grandmother’s side. According to Ancestry DNA, I’m actually doubly related to him, however I can’t actually find a blood connection to the Cherokee in his ancestry. It says his dad is a Colonel Kirkland and his mother a Raiford, but I’m not seeing where the Cherokee connection comes in. His wife was Lilly Berry Faw (Phau) b. 1758 Polk TN, d. Abt. 1851 also at Polk TN.

My great-grandmother was very obviously native in appearance, but so far “Cheese squire” is the only possible connection I’ve found on her side. Her name was Emma Hughes (b. 16 July 1911 in Swain Co. NC, d. 2000 Haywood Co. NC) and is connected to Kirkland via her mother Sarah Harriet “Hattie” Birchfield Hughes (b. 6 June 1882 Graham Co. NC, d. 26 February 1946 Blount, TN).

Any help would be greatly appreciated, thanks!