The Tipton Co. tngenweb site states that Randolph was established in 1827 (Post Office established in 1838) and is located on the "Second Chickasaw Bluff a little below mouth of Big Hatchie River". Cited are 2 sources for further information:
1) Wade, Wm. J., Notes on Randolph, TN (Memphis newspaper 1949, 7 pp) and 2) Ballard, Helen, Randolph, Tennessee:Rollin' on the River (self-published). Try the 1834? Tennessee Gazetteer for info and map. Current internet map sites (i.e. Map Quest) are sources for locating the area today.