When you get down to it, no. They don't. If you are feeding proper amounts there is no need to fast.
As carnivores, their digestive system is slow. That's why some people fast, to give them a day of rest from digesting. Also in an attempt to mimic a wild setting, though not completely accurate, times between meals can vary greatly depending on season.
Some dog experts recommend fasting dogs once a week, however as far as I know there are minimal positives to doing this. Same goes for betta.
On the other hand, some betta are prone to bloat (I'm noticing crowntails most often). I have a crowntail prone to bloat. He is fasted 1-2 days a week (usually once) and often is fed once daily. In this case it's important to fast a betta, when they have digestion/constipation issues.
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