I have an Amos Smith in my line & he had a son named Amos as well. I don't know a whole lot about them. They seem to have had some Darke Co., OH connections.
I have Amos Smith married to Elizabeth Ashby. Amos Smith b. 1779 and d. Nov. 1852, Grant Co., IN. Elizabeth Ashby b. 1788 in KY and d. May 1862 in Grant Co., IN. They had 12 children - I don't have a Nancy on my list of children. I have most of their children born in Miami Co., OH. One was born in Darke Co., OH in 1829.
I have Amos Smith, Jr., b. about 1820 in Miami Co., OH. He married Elizabeth Mayo in 1841.
Sounds like yours may be a different Amos Smith than these (?). Maybe by now you have found out more on your Amos Smith.
I'll post a bio I have on this Amos Smith from Randolph Co., IN - in a separate message.