How long is refrigerated fish safe to eat?

Probably a week to ten days, but that depends on the quality and stability of the refrigerator. Some older fridges do an "auto-defrost" cycle to eliminate frost in the freezer compartment, and this can have a detrimental effect on the quality of the food.

Smell it and look at it; if it smells OK and looks OK, it's probably still good. But remember the basic rule of food storage; "If there's any doubt, there's NO doubt - throw it out!"