If you strictly want to use the PPSSPP emulator on Android, you cannot play Sonic Mania. Instead, you can play the official PSP Sonic games, which are very similar in style.
The Best PSP Sonic Games for PPSSPP:
Guide to Setting Up PPSSPP for Sonic Games: sonic mania ppsspp android download free
You legally need to own the game to dump the files, but for the purpose of this guide, you will need a .iso or .cso file. If you strictly want to use the PPSSPP
Warning: Downloading ROMs and ISOs of games you do not own exists in a legal gray area. This guide assumes you are downloading free, homebrew content created by fans, not pirated commercial games. Guide to Setting Up PPSSPP for Sonic Games: