So I commented a couple months ago on a post about Ed Nygma/The Riddler that theorized about what might have happened to him post-Gotham and what his future interactions with the GCPD and Batman could have been like. Here's what I said:
I think that Ed's story is very tragic. He's my favorite character on the show, and I was always hoping that he would overcome his Riddler persona.
I have a personal fan theory that Ed's fight with the Riddler is far from over. In most Riddler appearances in media, he is very well known for the puzzling act of leaving clues to lead Batman to foil his own plans. Now of course, every adaption of Riddler has a reason for doing this, but it usually seems strange that he would willingly leave hints to lead to his own arrest.
I like to imagine that the Gotham's answer to that involves Edward, who is still within the Riddler's subconscious as shown in season 4. Edward is shown as someone who is trying to be a good person throughout his time on the show. Edward really just wants love and a genuine friend, though he usually tried to gain love and friendship through misguided ways. Still, to me, he doesn't want the Riddler to be in control because the Riddler resorts to murder and despicable acts for his own agenda. For example, nearly every murder that the Riddler commits is purposefully thought out while Ed's murders are more by accident. Ed doesn't want to kill or commit crimes to get what he wants, but the Riddler is completely fine with doing so.
Therefore, I believe that the Riddler continues to leave clues for Batman after the time of the Gotham show because Ed's still in there. Ed knows that the Riddler is evil. He wants to try to stop him while he is able to do so by leaving behind riddles and hints to what the Riddler is planning for Batman or the GCPD to discover without the Riddler knowing. The Riddler was mostly in control, but I always kept in mind that Ed was still in there as well. So in this way, I like to think he resurfaces in those little moments to help Batman and Gordon stop the Riddler's plans.
Of course, none of this was really explored on-screen, but if the Gotham story continued, I'd like to see this kind of thing.
While I also acknowledge that Ed wasn't completely innocent in any of the Riddler's or his own crimes, one of my favorite things about Gotham was how Edward still strived to do everything that he could to not let his demons win. I ultimately find his story tragic because we all knew who he was supposed to become, yet he still fought back against the Riddler anyway. I think that's why I like this theory that he's still fighting back against the Riddler on the inside, even though the battle is seemingly already lost.