What was your Grandfather's name and approximate birth year?
There was a William Beasley Sr. age 55 b. NC listed on the 1860 Barbour Co AL Federal Census - it doesn't give his middle name. But his wife is shown as Elizabeth age 46 born GA; Acy F. 23 (male); John 22; William 20; James 17; Mary 15; Sarah 12; George 10; Kansas 4. All the children are listed as born in AL.
The census ages are always risky, so don't consider them absolutely correct.