whales are not fish but are mammals but they live in the sea and i know the answerr to the question "do whales sleep" so i will pretend that thats what your meant.
Whales sleep with one half of their brain at a time. If a whale was to shut down entirely it would drown as they breath air. One half of its brain controls one half of its body which allows it enough movement to stay near the surface and to wake the other half to get air when needed. The hemispheres swap around so each part of the brain has a net total of a good nights sleep.
Fish? i dont know.