J. T. Barnhill is John Timothy Barnhill and son of Noah Hilary Barnhill.
The "Grandfather" referred to by J. T. was John A. Barnhill, son of John Barnhill who appears in the 1800 census in New Hanover County. John A. Barnhill moved his family into Bladen County after 1840 and prior to 1850.
John A. Barnhill fought at the Battle of Moore's Creek during the Civil War and was brother to my 3rd Great Grandfather, Alexander Barnhill.
According to the number of years above, the Barnhill families were in Pitt County, NC prior to 1730.