This is just a guess, but it might be a lead.I received this information several years ago, when I did a poor job of keeping sources, so I am not sure where it came from.
I am descended from James Adams who came to GA in the 1790's from VA.He was married to Jane (Jenny) Cunningham. They had a son, John C., from whom I am descended.
One of their other sons was Samuel who married Martha Ann "Patsy" Thornton.Samuel was born in 1784 in VA, before the family came to GA, and he died in Midway, Barbour Co., AL 6 Nov 1861.
Samuel and Patsy had children: Charlotte born c 1804 Sanfordc 1806 Josephc 1809 Thompsonc 1809 Eldridgec 1812 Jamesc 1814 Elizabeth Janec 1817 Marionc 1820 Jerimiahc 1823 Merialc 1826 Martha Annc 1828 Alfred Newtonc 1831
That gives you the James, Joseph and Thompson names and a James that was born near the time of your James.Thomson was Jenny Cunningham's mother's maiden name.
Since you are an Adams, have you considered taking part in the Adams DNA project?That would greatly help you narrow down your line.
Feel free to contact me if you have questions or want more info on the Samuel Adams family.