•1356-1358 Ivan Ćuz

I'm not having any sucess with the name Cuz. Googling Ivan Čuz turns up many references to lists of Croatian Bans, which don't give any alternate spellings or names that i can find.
The only other reference I could find of interest was to an Ivan Čuz dedicating a church in Ludbreški.
Searching for Ludbreški turned up a link to the Pécz family, specifically C3 Péter Ludbregi is the brother of the Palantine of Hungary (C1. Dénes, Nádor (Palatine) of Hungary, fl 1257-84.

On Geni Petar Ludbreški / Ludbregi has a son but the line ends there.

Dénes Pécz fl 1257-84 has a son, Ivan the Earl of Veszprém:
D1. János, Fõispán (Comes) of Veszprém fl 1292-1321

I'll leave this info here in case it helps later.