I have a betta fish that I got about a month ago, and just started noticing black patches on him, and one white patch underneath his gills. He still acts like his usual self, he still eats, and is pretty active, but I want to be sure he isn’t sick or anything. He is in a 3 gallon tank filtered and heated from 78-80 degrees, and I do 25% water changes every week.
Nothing visual on your beta would be concerning to me. Many fish exhibit color changes for years even after they are born and developed enough to be considered mature. I'm going to guess it's just his natural color developing over time unless there are other signs of stress or illness. If it starts looking like cotton or the texture of his scales or skin changes, that would be a sign of some sort of infection, but based on the picture, it looks like color only to me which should be fine.