Maybe this will help. William Beckham b. abt. 1612/19 in England m. Tabetha Randolph. They has a son (or brother?) Simon b. abt 1655 England m. Lydia. Simon and Lydia had William b. abt 1680 m. Phillis Randolph. This William and Phillis had William b. abt 1709 m. Phillis Mackey. This latter couple migrated to NC with family. One of their sons was Thomas, m. Mary Hughs.