There is a John Griffith's listed as having mail at the nashvill ost office 10/12/1805 vol.5 no.33 and alsovol. 5 no. 48

"Genealogical Abstracts from Tennessee Newspapers, 1791-1808.

I also found mention of the name Griffiths in Jackson county. Just that they lived next to a David Dixon and John Payton.

There are 100's of Griffith names and Green names in this book