Do water snakes stay on top of the water or underneath the water?

... depends who you call a "SNAKE". If you call "snake" longiformes FISHES, like eels (in fresh waters), or the conger (in salted waters): They are fishes, the have gills (scholar term is BRANCHIAE), thus they can "live" under the water. If you point at terestrial snakes that "can" swim or at some other which live most of the time in ponds or rivers or alongside, but have only aerial lungs or/and an oxygenation by the skin: Then the answer is no: They don't "live" under water; they just plunge into it, monenteanously, in apnea, to feed.