I just found some info on the Williamson Co., TN special collections dept who had a probate record for a Thomas Adams who died in 1823, and was listed as an executor named Wiley Adams.Also seemed that his son was Thomas and he could of had a son named Wiley.Hope this helps.
"The Thomas Adams on the Williamson County 1820 census did not have any sonsunder 16 years old which excludes him from being the father of Isaac and James G. Adams.However , you may have the right family in Williamson County just not the right generation. That is, the Thomas that died in 1823 may just be the grandfather of your bunch but it will take more research.I say this because Thomas Adams died before Feb. 12, 1823 (when Wiley Adams was appointed Administrator of his estate.) and in October 1823 James Adams, Isham Adams, Laban Adams, Isaac Adams, Thomas Adams, Wiley Adams, Susannah Pewitt, Joel Pewitt, William Harrison and his wife Nancy, John McNabb and his wife Winney, Marshall McNabb and his wife Polly, and Joseph L. Thomson and his wife Sally,sold their undivided interest in a piece of property to one James Wilkins, (Minute 7, page 213. )As you see they have the same names of James, Isaac, and Wiley, which were possiblyuncles of your James, Isaac and Wiley, and the Thomas was possibly the father of your James, Isaac and Wiley. "