What does 私様 means? I see that apparently this word is used by a character in a videogame called danganropa. It's a word like boku, atashi or something like that? Or it's something different? It's used to call yourself superior or something like that maybe? Maybe it's her nickname?

It's a sort of {}, though I don't any other character in fiction that uses it. {} makes her 'regal' personality sound both queenly and extremely arrogant, which is the exact vibe she is going for. Interestingly, in the first game she pairs it with more modern 'regal, haughty woman' speech, but in the second it's an older style. For example, in the first she would probably phrase 'I have been waiting for you!' as while using that personality, but in the second she'd phrase it as .