There are a few good 'DOTS' to 'CONNECT' in your family line, with what is known earlier.
(1) HICKS.ELIZABETH HICKS & your JOHN EDWARDS married 07 Jun 1849 is a good starter.PETER EDWARDS had several HICKS associations early 1800s in Williamson County, plus the following from over in Lunenburg County, Virginia.
21 Feb 1799.PETER EDWARDS and his wife FRANCES PARKS of Davidson Co TN to THOMAS EDWARDS of Lunenburg County, for L20, 45 1/3 acres in Lunenburg County, adj. ZACHARIAH DAVIS, ROWLAND WARD, MARY EDWARDS, & land where ELIZABETH EDWARDS now lives. Wit.: JOHN HICKSSig PETER EDWARDS JAMES HICKSFRANCES P. EDWARDS FRANCIS EDWARDS Recorded 13 Sep 1799. Source:June Banks Evans, Lunenburg Co VA Deeds Bk 18.US/CAN 975.5643R2ev.18-19. page 46 (orig. page 146).
(2) FRANCIS EDWARDS (male) Witness FRANCIS EDWARDS in the above deed is a younger brother of PETER EDWARDS, and he died about 1808, possibly unmarried, and his estate is referenced in both Williamson County, Tennessee, and Lunenburg County, Virginia.(THOMAS & MARY EDWARDS are also PETER's siblings. ELIZABETH is likely the widowed mother of the bunch.) ELIZABETH SMITHSON was a daughter of FRANCIS SMITHSON (c1706-1783) of Lunenburg, VA, and so FRANCIS EDWARDS (died c1808) is his grandson and name-sake. Your JOHN EDWARDS had a likely brother FRANCIS or FRANKLIN EDWARDS born c1821.The name carries on down...
(3) SAMUEL T. EDWARDS, possible brother to PETER EDWARDS Jr. FRANCES PARKES JETER was a daughter of SAMUEL JETER who died in Amelia County, Virginia, about 1794.So this SAMUEL T. EDWARDS might be SAMUEL JETER's grandson and name-sake, on PARKA's side of the family.
QUESTION.You say that"The 1850 census reflects John, Francis and their wives all living in the household of Sarah and her husband James A. Neely."
Please share that Census with me, by e-mail, easier for me to study the evidence.
RULON RULON N. SMITHSON 804 East Orchard Drive Pleasant Grove, UT 84062