The will of William Cooper mentions:
Daughters: Martha and her children & Nancy.
Sons: John, Adam, Alexander, William & Thomas
(His wife, Nancy, predeceased him.)
The 1800 census shows 5 sons so it is possible that these are the only sons of William & Nancy. Not yet proven.
It is said that William inherited land from his father, John (1721-1801), but also purchased many acres prior to his father's death in 1801. William left the land to his son, Alexander, who was to care for Adam. John and William moved to Mississippi.