Bettas are labyrinth fish, which means they can breath air from the surface, not have to take it in through its gills from the water like most fish.
But the bettas you see in tiny containers in fish shops are only meant to be there
temporarily; it's not supposed to be home for life. The fish may survive those conditions, but it won't be living a happy life, which is what we want for our pets, even if they are 'just fish'.
There are lots of tiny fish that you can keep, but they will all, if they are to thrive, not just survive, need a proper tank with a filter and heater.
If you're going to get a tank, get one of around 50 or 60l; that's a size that many fish will be happy to live in for their whole lives. Any smaller and you're likely to end up with cramped, unhappy fish. We don't know the hardness of your water, so I wouldn't recommend any fish species to you yet, but there will be lots to choose from
If you find out the hardness of your water (it'll be on your supplier's website), then we can recommend species, but you'll need to get a tank and cycle it before you can have fish anyway.