Do fish sleep?

Yes, fish sleep. But they don't close their eyes, they don't snore, and they don't sleal their partner's blanket. If they dream, we don't know what they dream about. Fish sleep differs from human sleep; they simply reduce their activity and metabolism, although many keep moving to maintain the flow of oxygenated water through the gills, allowing them to breathe.
Because their eyes are always surrounded by water, they don't need to moisten them as we do when we blink, so most fish have no eyelids.