Fury also said he had "the psychological edge" because Wilder's nickname of the 'Bronze Bomber' means "a third-placed man."
When Wilder later warned his opponent that on the night of the fight "you're not going to be looking into the eyes of Deontay Wilder, you'll be looking in the eyes of the Bronze Bomber - you're going to feel him too", Fury asked if he was talking about "an alter ego" or "a spirit".
He added: "You're already beat. Anyone who has to have an alter ego and not be themselves in there, and try to get in someone's mind like that - you can't beat me."
Wilder subsequently chanted "there's only one Bronze Bomber" a number of times at Fury, to which the latter responded: "I can see it now, the alter ego coming through. You and your alter ego are a pack of bums.
"Where are you from? Who are you? You're a bum from Alabama who is getting knocked out."
As the programme drew to a conclusion with both men rising from their seats, Wilder said he was going to "baptise" Fury, who called the the 32-year-old "a skinny little man" and "a basketball player."
:: Fury v Wilder is live and exclusive on BT Sport Box Office, December 1st. For more info go to btsport.com/boxoffice