The William that you are looking for was a brother to my 3rd great-grandfather Peter. Their father's name was William also. I haven't been able to find out anything on him except that he came from Rowan Co., NC sometime around 1812. That year is a estimate by my dad based on the ages of William's children, and place of birth.
The eldest William and Andrew Criswell can be found in the North Carolina 1800 census in Rowan County. We believe that William Sr. and Andrew were brothers, but we can't be sure.
I hope this has been helpful. If you have any more questions I'll help all I can.