EM0280729, it sounds like your sister's betta has some ammonia poisoning. He's twitching because the ammonia in the water is burning him. You can help him this way: first, change 25% of his water now. Tomorrow, change another 50% of his water. On the third day, change 100% of his water. After that, get on a regular schedule of frequent water changes.
In a 1 gallon bowl, you will need to change his water at least every other day, no less than 50% each time. While a gallon bowl is fine for a betta when the water is changed frequently, you may want to consider upgrading to a 2 gallon tank or more because it is, as Waterbottle2 stated, easier to heat. Your guy needs temps of at least 78-80 degrees farenheit.
Hope this helps.