The Smith family from the Mayflower to Smithville, Tenn.

I am looking for the ancestors of Ransom Smith born April 11, 1761 in Hanover Va. I know he also lived in Granville N.C. and
married Elizabeth Morse there August 26th 1783. They also lived
in Campbell co. Tenn & Marion Co. Tenn. My great-grandfather was one of their children, His name was Elmais. I have a lot of information on decendents and will be happy to share. but am having a problem finding ancester of his. Any help appreciated.
I have been told there is a connection of some sort with Capt. John Smith, Maybe his brother, cousin, not sure of this but it
has been handed down in the family.
Thank you Beverley Keane