William (T.) Watkins who married Eliza Linton was born in about 1809 to William Watkins and Anna Rawlins Watkins of Poquoson. He is listed in the Bible belonging to the Freeman family (William's daughter Martha married John Freeman) along with William and Anna's other 6 children. He is also in William's 1820 York County census, along with his brother Thomas Vincent, in the age 10 - 15 group. On the other hand, Thomas (Aduston) Watkin's 1820 York County census only lists 2 males less than 10 years old (Henry and ?). For those reasons, I think your William was William and Anna's son. Hope this helps!
Chris