Theodore Roosevelt was the guy who started the Bull Moose party, and cost Taft the election. Wilson (whom I hate, but one who was probably more competent than Taft) won.

William Henry Harrison, John Tyler, Zachary Taylor, Milliard Fillmore, Thomas Jefferson*, James Madison*, James Monroe*, John Q. Adams*, John Adams

Those marked with * were Democratic-Republicans so i'm not sure if they count

Democratic-Republicans were one of the 2 main parties of their era. For that matter, the Whigs were, too (the Republican Party grew out of the Whigs, so if anyone could be argued to be a 3rd-partier, it would probably be Lincoln, but then again, the Republican party was well-established and one of the dominant 2 by that point.)The rest were all in parties, too, except Tyler, who was a Whig, but got kicked out of the party because they hated him, but that was mid-term, and wasn't even elected (He only got the office because Harrison died a month into office).

they were all members of a third party of their time

Bernie Sanders, Joe Lieberman, Lincoln Chafee, Charlie Crist.
Dude are you serious?

He's talking about presidents.