You are apparently looking for one of the children of Jeremiah Mize and Elizabeth Gilliland. Here's what I think may be accurate: family in North America started with James in VA who had two sons Jeremiah b. abt 1698 and James b. abt 1700. That Jeremiah married Grace and they had children Joshua b. 10 Mar 1724, Robert b. 10 May 1721 and John b. 1732. Grace apparently died and he married Tabith Edmonds and they had at least 4 children. Joshua b. 10 Mar 1724 married Martha Patty and they had at least 10 children including Jeremiah b. after 1756. He married Elizabeth Gilliland and they had Isaac Mize b. Abt 1802, Margaret "Peggy" Sarah b. abt 1800, William Riley b. 01 Mar 1801, Elizabeth b. abt 1806, and Lucy b. abt 1816 all apparently born in Pulaski Co, KY.
I have seen William mentioned, but I've been concentrating on Isaac. I think you should be looking in Pulaski Co., KY if the family I've detailed includes the William you are seeking. I am interested if you've found anything on Isaac.