Your PSN account would have to be linked with an EA Account in order to play any EA games online. If you've already been playing Apex Legends it sounds like your PSN ID was probably linked with an EA Account a long time ago.
Usually that error message just means that you'll need to reset the EA Account password. If you haven't already, can you give that a shot to see if it helps? You can find more info on how to reset it over at the EA Help website.
Let me know if you're still having trouble logging in after that. Thanks!