Fischer had a chess variation (chess960) but I cannot find any mobile app to play it.
Does anyone knows where I can get the best software (if possible free or cheap) to play it?
There are a number of websites and tools listed on the Chess960 wikipedia page. Scroll to the bottom for the complete list. These should all be playable on your mobile device.
2012 there was chesscube i think...oh wait i think i remember in 2014 they didn't have 9LX in their app. RIP chessube
2021 this is very moot of course. lichess, chessdotcom, chessvision (using lichess), etc
If you use iOS there’s Chess Studio from AppStore which it’s great and have the 960 board positions to play against machine! Which is Stockfish!