I do believe Cora Applegate Foster is one of ours. My information varies a bit from yours, however. It is based on the the Absalom Pettit Bible Record of Mt. Magnolia Plantation, Warren Co., MS.
It reads, in part, Horace F. Foster b. 17 Jy, 1870, married Lucy Blanche Applegate in 1892. Children : Cora Applegate b. 1896 Nellie Foster b. 1898 Blanche Foster b. 1900 H. F. Foster Jr. b. 1902, married Opal ___ m. __ 1925.
I assumed that these births and the others mentioned in this Bible all took place in Mississippi, but I may be mistaken in this. I have much more information about this line of Fosters. Get back to me and we can exchange notes.