One idea could be that Batman discovers a new Kryptonian weapon that Superman unknowingly has a weakness to. This weapon was hidden on Earth long ago by a rogue Kryptonian. Batman then has to decide whether to use this knowledge to defeat Superman or find a way to help Superman overcome this potential threat together.
Perhaps in the fanfic, there is a new villain who can absorb powers. He starts by absorbing some of Superman's powers and then frames Batman for the attacks on Metropolis. Batman has to prove his innocence and also find a way to stop the villain before he becomes too powerful by stealing all of Superman's powers.
A really cool plot could be a 'what if' scenario. What if Superman was raised in Gotham instead of Metropolis? How would his powers and values be different? And how would Batman react to having a super - powered being in his city from the start? In this fanfic, we could explore their relationship in a completely new light.
One idea could be that a powerful new villain emerges who has the ability to manipulate both Batman and Superman's minds. This forces them to fight against each other while the real enemy is pulling the strings. Another could be a situation where Gotham and Metropolis are in a territorial dispute, and Batman and Superman initially take sides based on their cities, but then realize they've been played.
A cool plot could be that a powerful alien race arrives on Earth and offers a deal to the world leaders. Batman is suspicious of their motives and starts investigating. Superman, on the other hand, is more open - minded at first. This causes a rift between them. As Batman uncovers more evidence of the aliens' true intentions, he has to convince Superman. In the end, they join forces to stop the aliens from taking over the Earth.
Perhaps Batman has teamed up with some of Superman's other foes who have knowledge of his weaknesses. For example, Lex Luthor could provide Batman with technology or information that gives him the edge. Also, Batman might use psychological warfare on Superman, playing on his insecurities about being an alien among humans.
A plot in the fanfiction could be about Lois Lane being the key to preventing the fight. She discovers a secret that proves both Batman and Superman are being used in a political game, and she has to convince them to trust each other. In this way, it would add more depth to her character as more than just a damsel in distress. For example, she could use her journalistic skills to uncover the truth behind the forces trying to pit the two heroes against each other.
One idea could be a story where Batman and Superman have to team up to stop a powerful new villain who is using kryptonite - based technology. This would put Superman at a great disadvantage and force Batman to use his detective skills to find a way to neutralize the threat.
One plot idea could be that an otherworldly threat emerges that only their combined powers can stop. They have to put aside their differences and work together seamlessly. For example, a powerful alien race plans to invade Earth and they need to use Batman's strategic mind, Superman's super strength and Wonder Woman's combat skills.
One idea could be that Batman and Superman have to team up to stop a new villain who has the power to manipulate time. This would put their different approaches to justice to the test as they race against the clock.
Here's an idea. There could be a powerful magical artifact that surfaces in both cities. It has the power to change reality. Superman, being a man of science, is initially skeptical about its power. Batman, on the other hand, has seen enough strange things in Gotham to know it's dangerous. They have to overcome their differences in beliefs as they race against time to stop different factions in both cities who want to use the artifact for their own gain. Along the way, they also learn more about each other's worlds and form a stronger bond.
In a fanfiction, perhaps there's an apocalypse scenario where Superman is infected with some kind of kryptonite - based virus that makes him go berserk. Batman has to find a cure while also keeping Superman from causing too much damage. At the same time, they are dealing with the general chaos of the apocalypse, like gangs taking over the city and other villains trying to take advantage of the situation.