I looked on the DAR web page and found a Jeremiah Smith married to Jemima (No Surname listed) Born Abt. 1755 died Abt. 1800. State of Service is Listed as South Carolina. State of Death Listed as Greenville District South Carolina. Could this be your Patriot? If so, I would try to look for a Probate record listed for him in South Carolina. Your best bet would be to find a Will listing heirs to the Estate. You might try finding one for his wife Jemima too, by looking in Louisiana and Mississippi. There are three people who are listed as descendants of this Patriot, through a son also named Jeremiah. The generations listing for each person shows a common thread with your info. They all show the families as being from South Carolina-to Georgia-to Mississippi. You can Purchase a record copy of a previously verified application on the DAR website. It can be used as supporting documentation to help link to a patriot. It costs ten dollars. I don't know if this helps at all, I wish you luck.