J'zidzo is a Khajiit thief who resides in the town of Split. He shares his name with an alternate version himself in the same town. Despite having the same name and appearance, they share no other traits besides their hatred for each other.
Both of the J'zidzos want to see the other die, but are unwilling to deal with the price of killing "themselves" and being sent to the Hill of Suicides. They will send the Hero to Horkvir Bear-Arm, and state that he has a plan to fix the problem.
Depending on which side is chosen, one of the J'zidzos will be killed, making the other happy to finally be the only one left.