how to find great grandmother name/records, possible native Cherokee

I want to learn about my paternal grandmother who, story says, was Cherokee and died shortly after childbirth to my grandfather in White County, TN.  My grandfather lived with an aunt/uncle (I think it was his father's family/brother) and I found my grandfather on the 1920 census in the household with family of the aunt/uncle.  What's my best next step to find out more about my great grandmother?