G (or C?) W Ross is credited with adapting Jack Hall and changing the name to Sam Hall in the 1840s. I suppose if you were to look for "the authentic version" of Sam Hall if there is such a thing, it would be his assuming it does exist written down somewhere. To quote Kidson, he sang it "with a very blasphemous chorus". I'm not sure whether that balsphemous chorus included the f word - my guess is it didn't.

Coming back to Jack Hall, Bruce Olson noted in one of the many Sam Hall threads here:

"The original broadside version is lost, and the best text we have is a traditional one in Cecil Sharp's 'One Hundred English Folksongs'"

Going by Contemplator, Sharp believed the song to have been written before 1719. Hall was executed in 1701.