The answer is yes, they do. If your betta have plants or cave inside his aquarium, that's where he usually sleeps. He will act as if he's startled if you light him at night. Why night? Because it's hard to sleep for creature that don't have eyelids. Betta fish doesn't have eyelids and therefore they choose to sleep when the lights go out.

Sometimes they take naps during the day right in-between the leaves. So be sure to have leaves in your aquarium.

Betta fishes are diurnal, meaning that they are active during the light hours. When they do rest, most diurnal fishes will be very pale. Usually they rest when the light is out and the surrounding is dark.

On the contrary, nocturnal fishes will look for dark areas and often rest there, and when other fishes rest at night, they will come out and feed.