The Zombie Fish is a quest item that is needed for the Angler. This Fish is obtained by Fishing in a Forest. It may be caught during the day.
"You won't believe it! I caught a fish in a forest at night that was already dead! Then it tried to eat me! I threw it away and ran! Now I want to stick it in someone's dresser to see what happens, so go fish it back up for me will ya?!"