You can air-drown a fish by taking it out of the water, or if you keep a fishtank and don't maintain it properly, the oxygen levels can get too low, so yes, you can drown a fish, even under water. Also there are fish such as bettas (aka siamese fighting fish) which do get oxygen from the water, but also from the surface, so if they can't get to the surface for one reason or another, they would most likely drown.