I think I can help you because I am a direct descendent of the people I believe you are referring to. Cornelius Mitchum was born in 1795 and lived in Williamsburg County, SC. He died in 1868. His wife was called Patsy and her maiden name was Guess. He did have a son named George but his middle initial was not R. His full name was George Keels Mitchum. I have seen the middle initial mistakenly listed as an R and an H but I am 100% sure his middle name was Keels. I Cornelius's father was named Eleazar Mitchum and he was born in 1771. I know more about this family if you have more questions.