You should probably get the 1820 Ross Co., OH, Census to see which ADAMS families were there at that time.
"Gateway to the West" has some early Ross Co. men named ADAMS, some too early to be yours, but perhaps yours joined their relatives.
Ross Co., OH, Court Order Book, June 1799, jury duty, John ADAMS.
Court Case, John BROWN v. Samuel SMITH, filed Dec. 1799.Note by Reuben ADDAMS [?]made to order of Samuel SMITH, Esq., 24 S 1799 at Chillicothe in favor of John BROWN,to bearer 164 gallons + 3 quarts of whiskey on Reuben's account, not delivered, case discontinued, costs paid by Reuben ABRAMS [?].
Filed Dec. 1799 & continued to June 1800, James LAWSON [late of Hamilton but now of Adams Co.] v. Robert ADAMS [late of Hamilton but now of Ross Co.], jury for the defendant, plaintiff to pay costs.
Ross Co. estates, Hugh ADAMS, 1814, Case 20.Isaac H. ADAMS, 1817, Case 22.Robert ADAMS, 1818, Case 21.