The only record I found for you was in "Family Search" I found a marriage in Barren Co. KY for Gabriel Pullium and Nancy Reynolds on 10 Sept 1827.
The only child I saw was of a Garland Pullium who was born in OH in 1832 and died in the civil war (WV) on 19 Sept 1864. As there is no documentation verifying this and no mention of any records pertaining to Garland, I will take this only as face value. I have added his marriage to Nancy on the profile page.
M. (Greeter)