If you want a completely original FG built for mobile there is Konsui Fighter. Real small community though, it's basically a Discord fighter right off the bat. Other than that, there's the Street Fighter 4 CE port. It's the full game, but the caveat is it looks terrible and runs at 30fps since the port came out way back when phones weren't as powerful.
All the other FG "ports" are original gacha games made for mobile, those being Skullgirls, the 2 Injustice games and Mortal Kombat. If you don't mind the gacha I'd recommend Skullgirls, it retains the most FG mechanic from the original while being made with a touchscreen in mind, the NRS games are just tap to attack and occasionally use specials, you have to mostly rely on your characters' stats to win.
As for emulation, if your phone is powerful enough, nab Eden and use the online room feature. Capcom and SNK basically ported their entire FG catalog to the Switch.