Tracing Native American Roots

I’m looking for information on my Great Grandmother Mae or May Duncan. I am told she was Cherokee and was disowned because she loved a white man, his name was Everett Hamilton. She died in 1961 in Rush, Kentucky (Boyd County). She was my Dad’s grandmother and for whatever reason his side of the family won’t give me any information or help. Dad’s mother’s name was Evelyn Hamilton, I believe she was born in the 1910’s.