In this fanfiction, perhaps the Ministry has misused its power in relation to Hogwarts. For example, they might have imposed unfair regulations on the school that Harry believes are harming the students. So, he sues them to fight for the rights of the students and the proper running of the school. Another possibility is that the Ministry has been involved in some sort of cover - up related to dark magic activities, and Harry, being the hero, wants to expose them through a lawsuit.
The fanfiction might involve Harry Potter suing the Ministry over issues regarding the treatment of magical creatures. He could be fighting for the rights of creatures like house - elves or werewolves who are often discriminated against in the wizarding world. Harry, having experienced discrimination himself, might see it as his duty to stand up for these creatures. He may also be suing because the Ministry has been interfering with his attempts to promote better understanding and co - existence between different magical species.
Maybe Harry Potter decides to sue the Ministry because they have been withholding important information about his family or his true destiny. It could also be that the Ministry has been unjustly persecuting him or his friends, and he decides to take legal action within the wizarding world's framework.