Carroll Family Genealogy Forum
If you check further down on the census you will find a William Carroll, wife Quilly, and daughter Jane. William is 30 which leaves open the possibility that he was a son of James. Not sure or proven though.
Now my branch has the name Piety in it. Again here it is possible that James was a son of William and Piety Fluellin. Not sure, as he would have been the only known child not mentioned in William's will. But according to the earlier census' William did have four other children. Two boys and two girls. Perhaps all by his first wife who died before 1797. If James infact was born in c1800 then could be the son of William and Piety. Or Piety was his step-mom.
Just thought to give you something to ponder.