1759) and William Barton (1754–1817), a lawyer who designed the Great Seal of the United States.

Among his siblings was older brother was William Paul Crillon Barton, the medical botanist, physician, professor, naval surgeon, and botanical illustrator.

His uncle, Benjamin Smith Barton, was an eminent medical botanist and vice-president of the American Philosophical Society.

[7] Through his daughter Alice,[8][9] he was the grandfather of John Rhea Barton Willing, who did not marry;[10] Susan Ridgway Willing, who married Francis Cooper Lawrance Jr.;[11] and Ava Lowle Willing, who was married to John Jacob Astor IV (son of William B. Astor, Jr. and Caroline Schermerhorn Astor) until 1910,[12] and, thereafter, to Thomas Lister, 4th Baron Ribblesdale.

[13][14] In 1877, his widow Susan Ridgley Barton endowed "The John Rhea Barton Professorship of Surgery," at the University of Pennsylvania School of Medicine, the first endowed chair in surgery in the U.S.[15]