Fish sleep in the water. They sleep with their eyes open because they do not have any eyelids (some sharks do, but fish do not). The amount of time a fish sleeps varies depending on the type of fish.
Every species offish is different in the way it sleeps. Some sleep while still swimming (which makes it difficult to identify when they are awake and when they are asleep). Other species of fish burrow themselves in the corral or rocks along the bottom of the ocean and are completely still except a movement of a fin here or there to keep them upright.
However, all fish have some sort of movement while sleeping. They have to continue moving in order to keep water flowing through their gills. If water is not flowing through their gills, they cannot pull the oxygen from the water, and will suffocate.