I believe that this James Adams was married to Frances Herndon.Some reports show that he is the son of James Adams and Jane Cunningham.I am almost postive that this is INCORRECT.Although I have no proof.
See posts 13423 and 13427 on this forum about James.
The source that I have seen that shows James who married Frances does not show a son John Jefferson.
There was a James Burton Adams, son of Thomas Adams and Sarah Ford, who was also born in 1795.I do not show that he had a son John Jefferson either.
Good luck and if you figure this out, I would like to know the correct answer also.