The paradox brothers only appeared in 2 episodes. one was when yugi and his friends were trapped by cardboard cutout of a boulder, and the other one was when

they were on a helicopter having flashbacks

They are basicly a gay(as Joey calls it) rhyming people. They rhyme everything, and it really gets annoying. One rhyme was:

I guess we ran out of luck!

Its just a card game who gives a f--k!

and apparently, if you look at cardgamesftw's other account, ninjabridge, the "10th anniversary abridged movie", there is a 3rd paradox brother, but never rhymes or says hes related, but his name IS paradox...

for more information, please watch YGOTAS episode 35: A tale of two journies and YGOTAS episode 13, busted rhymes.