Its likely either a bacterial infection or fungus. Is your fish suffering from any other side effects? Such as clamped fins, laying on bottom of tank or on decor, or not eating/no interest in food? Without a picture its hard to say for sure whether its a fungus or a bacteria but there are a variety of medicines sold for fungus and bacterial infections for fish. White fuzz is most likely a fungal infection. The only way to eliminate is to get anti-fungal medicine from a fish store. Stay away from bettafix/melafix. It’s a treatment based off of palm oil and it can harm the labyrinth organ of your fish.I’d recommend Jungle Fungus Eliminator, which you can order online and find in some pet stores. Most fish/pet stores do carry some kind of anti-fungal/antibiotic fish medication. I’d start treating the tank with aquarium salt as well. This can be purchased inexpensively at fish stores, the dosage is 1 tsp per gallon. Be sure to mix the salt in treated (dechlorinated) water before adding it to the tank, as the salt crystals can burn the betta if not mixed and the salt won’t mix properly with the water in the tank unless you dissolve it before adding it. And keep in mind that salt does not evaporate, you can only take salt away from the tank by doing water changes. Your betta should have a filter in its tank, along with a heater that heats the water to somewhere between 78–80 F. I’d recommend a minimum tank size of 2.5 gal, smaller tanks are actually harder to maintain than larger tanks. In any tank under 10 gal you need to do water changes often, at least ~20% once a week.