The piece of evidence that proves my relation to him is a letter written by my great-great-grandaunt, found in the Civil War Widow Pension Files for the wife of the outlaw, saying that he was her brother, was born in Ireland, came with the family to Carthage, Illinois, fought on the Union side in the war and moved to Texas, marrying Ethelena Iola Hall. As I said, if this is accurate, it proves my relation to him.
Here's what I found in my search for descendants. First, two years after his death, in the 1880 US Federal Census, I find his wife and three sons still living in Kimble County, Texas.
someone's tree on FamilySearch has him dying in Los Angeles, California in 1922.
Thomas William Doran is found in the 1920 census living alone in San Bernardino, California:
Find-A-Grave memorial shows that he died in Deming in 1955. His obituary says his only survivor is a cousin, Mrs. Perkins, of El Paso.
The youngest son of Tom Doran and Ethelena Hall was John Hale Doran. I found him in the 1920 US Federal Census living in San Benito, California with his wife, Blanch:
Find-A-Grave memorial shows that he died in 1940 and is buried in Los Angeles.