Lex Luthor is often an interesting character in such fanfictions. He might be the one pulling the strings behind the scenes, fueling Batman's distrust of Superman. Another could be Alfred. His wisdom and influence on Batman can add depth to the story. He might try to talk Batman out of fighting Superman or help him in a more covert way. And then there's Wonder Woman. She could be caught in the middle, trying to mediate between the two or having her own motives for getting involved in their conflict.
The Joker is a character that can make things really interesting. He might see the chaos of Batman and Superman fighting as the perfect opportunity for his own evil deeds. He could also be the one who plants false ideas in Batman's head about Superman. Lois Lane is also important. Her relationship with Superman and her journalistic instincts could play a role. Maybe she's investigating why Batman is after Superman and uncovers some hidden truths. And don't forget about Oracle. She could be providing Batman with crucial information during his fight with Superman.
Alfred Pennyworth is quite popular too. He can offer his wisdom and support to Batman, and his interactions with Superman can be both humorous and heartwarming. He's like the glue that holds things together in the Batcave, and his presence can bring a sense of home to the story.
Lois Lane is often a popular character. In fanfiction, she might play a crucial role in mediating between Batman and Superman or getting involved in their adventures in a more hands - on way, using her investigative journalism skills.
Wonder Woman could also be involved. She might be caught in the middle, trying to stop the fight at first. But if she realizes that Superman is being a threat for some reason, she could side with Batman, or at least not interfere in Batman's attempt to defeat Superman.
One popular plot could be that Batman discovers Superman has been mind - controlled by some villain. So, in order to save Superman and the world, Batman has to fight him. Another plot might involve a misunderstanding. Maybe some false information leads Batman to believe Superman is a threat to Gotham, and he takes action. There could also be a plot where Batman is pushed to his limits by some external force that makes him see Superman as an obstacle, and he uses his wits and skills to take on the Man of Steel.
Catwoman can also be a popular character. She could be in a love - triangle situation with Batman, and her thieving ways might put her at odds with the female Superman who stands for truth and justice. There could be some really interesting interactions between the three of them, like Catwoman trying to steal a valuable item that the female Superman is protecting, while Batman is caught in the middle, not sure who to side with at first.
Alfred is always a likely ally. His knowledge and experience can provide valuable support to Batman. Also, Oracle (Barbara Gordon) could be an important ally, using her hacking skills to disrupt any technology Superman might use or to gather information.
Harley Quinn is quite interesting. She's caught in the middle between her love for the Joker and her own sense of self. Commissioner Gordon is also important. He's the one who often has to deal with the aftermath of Batman and the Joker's battles and is a symbol of the law in Gotham.
It really depends on the comic's storyline and the creative direction. Sometimes Batman uses his strategic mind and gadgets to defeat Superman. Other times, the outcome is less clear-cut and influenced by various factors within the comic's universe.
Catwoman can also be a popular character. Her ambiguous moral standing and her relationship with Batman can create interesting sub - plots in the fanfiction. She might get involved in a scheme that involves both Superman and Batman, either as an ally or an adversary depending on the story.
The Mayor could be a key character. He might be the one promoting Batman's image in the city, seeing him as a way to boost morale. Also, there could be a journalist who is always trying to get the inside scoop on Batman and in the process, shows the city's fascination with him.