I am an Awtrey decendant. According to my records John F. Awtry (Awtrey) was the son on John B. and Martha S. Awtry. He was born 9 Jan 1826. He was educated principally at an Academy in Troup County. On 20 Mar 1853 he married Mary E. Green in LaGrange, Troup County, Georgia.

These are the only Awtreys that I know of that lived in Troup County and by the dates they could be the parents of your g-grandmother.

Perhaps if you search the census of Troup County, Georgia for 1860 and following you can find the children listed.