So obviously this Josiah Bartlett isn’t the guy on The West Wing, in part because President Bartlet is fictional. (Okay, maybe entirely because of that.) But he is supposed to be a direct descendant of the Founding Father. Why, and when, the terminal T dropped off was never explained.
Anyway, Josiah Bartlett and John Langdon both arrived in Philadelphia from New Hampshire as delegates to the Continental Congress, and they both fought in the war, plus they were around for the Constitutional Convention—so there’s a lot of history between them.