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.
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.
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.
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.
Often it starts with mutual respect. They recognize each other's abilities and dedication to justice. For instance, Superman respects Batman's ability to fight crime without powers, and Batman respects Superman's selfless use of his powers.
One possible reason could be mind control. Maybe some villain has taken over Superman's mind and made him do it. Another reason might be a fundamental difference in their ideologies that has escalated to the point of no return.
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.
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.
It's more modern in terms of art and storytelling. The New 52 version has a different aesthetic compared to older comics. It often has a faster - paced plot.
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.