Yes, there are quite a few. Some explore a different side of the Joker where he has a moment of redemption and saves Batman. It often plays with the complex relationship between them and the idea that even the 'villain' can do a heroic act.
One common theme is redemption. It shows that even a character as chaotic as the Joker can have a moment of good. Another theme is the blurred line between hero and villain. It makes readers question if the Joker is really a villain in that moment.
Yes, there might be. The Naruto fandom is quite large and diverse, so it's very possible that someone has written a fanfiction with such a plot. You can try searching on popular fanfiction websites like FanFiction.net or Archive of Our Own (AO3).
The plot could start with Harry somehow ending up in Gotham. He notices the Joker's chaos and decides to intervene. Harry might use his invisibility cloak to get close to the Joker without being detected at first. Then he could start using his magic to slowly disrupt the Joker's evil plans.
Well, it could happen in a world where magic and the chaos of Gotham collide. Maybe Harry uses his magic to get into the Joker's mind and find the good that's left in him. He could use a spell like Legilimency to understand the Joker's past traumas and then use healing magic to start the process of redemption.
One common theme is the exploration of madness. Since the Joker is known for his insanity, OC characters often get caught up in his world of chaos and have to deal with their own sanity being tested.
One great 'Joker OC Harley fanfiction' could be 'The New Face in Gotham'. It's about a new original character who gets involved with the Joker and Harley's chaotic world. The story has great character development for the OC and shows how they interact with the iconic duo.
The 'joker oc daddy fanfiction' might be a creative exploration of the Joker's character through the lens of a new, original character. The 'daddy' concept could add an interesting layer of complexity, perhaps showing a side of the Joker that is different from his typical villainous self. It could involve stories of the OC getting into all sorts of adventures or misadventures with the Joker, with the power dynamic between them being a key aspect of the narrative.
Their relationship would become more complex. Batman might start to see the Joker in a different light, perhaps as a victim of his own madness rather than just a pure villain. The Joker, on the other hand, might be confused by Batman's act of saving him and could develop a strange respect for Batman, or he might try to use it to his advantage in some new, devious plan.
One common theme could be the power dynamic between the Joker and the OC. Since the Joker is such a complex and powerful character, exploring how an OC interacts with him in terms of power can be interesting.