Have you done the Ancestry DNA test? Assuming that Thomas Beason is your great-great-grandfather, Ancestry DNA now has more than 3,000,000 tests in its database. So - descendants of your Beason great-great-great-parents, would be your fourth cousins. You have a 50% chance of matching a fourth cousin. So - if the Beasons had a large number of descendants, you might have some interesting matches through them.