Hi. Sorry to come to this discussion so late. I just joined Ancestry.com.
The Andrew Cookson who married Barbara Castetter is my ancestor: Andrew Cookson > Andrew Jackson Cookson > James Melton Cookson > Charles Cookson > Orin Cookson > Rod Cookson > me. My father Rod Cookson collected a fair amount of information about this line of the family.
We have never been able to find Andrew Cookson's birth notice or immigration records. The 1790 birth date is rough at best--unless someone has information that we don't. We also suspect he might have been born here in the U.S., though without any documentation on his birth or who his father is, we just can't say.
For various reasons we suspect that Andrew Cookson was the brother of a Joseph Cookson--though we can't prove it. Pete Cookston did the genealogy of the Joseph Cookson family line. The Cookston family started out as Cooksons and later added the "t" to their last name. Joseph married a Cherokee woman and migrated west on the Trail of Tears, settling into Oklahoma. My ancestor, Andrew Cookson, went northward up into the Indiana region. My ancestry DNA results had 0% Native American genes. So we would be cousins of the Cookstons at best.
(Pete Cookston and his family believe they have identified Joseph Cookson's father. But the person they are referring to was born in 1710, which would have made him 80-88 years old when Joseph was born. So I personally don't think he's the father of either Joseph or our Andrew Cookson. He might have been the grandfather...but there is not a shred of evidence for that.)
My father and I have accumulated the names of several Cooksons in the southwest United States in the 1700s. But we have no documentary evidence that any of them were Andrew Cookson's father. Given the poor record keeping of those days in the rural areas, and the destruction of some important early records by the British during the revolutionary war, it may never be possible to firmly document who Andrew Cookson's father was.
Having said all of that, I would love to learn what other people have found.