Adrien might join his father out of curiosity. He has always had questions about his father and his actions. By joining him, he hopes to get answers to all those unanswered questions and to really know who his father is as a person.
Maybe he realizes how stressed his father is and wants to ease his burden.
Adrien would probably feel a mix of emotions. He'd likely be nervous as he approaches the prison, not knowing what to expect. Once he sees his father, there could be a sense of sadness, especially if his father looks different or broken. He might also feel anger, thinking about all the wrongs his father has committed that led to this situation.
Marinette might also play a role. Even though she doesn't have direct knowledge of Adrien's family at first, she is very observant. She could notice something odd about Adrien's behavior when he starts to search for his father's wish and offer her help. Together, they could piece together the mystery from different clues around the city.
Adrien could meet other mysterious figures in the lair. It could be an old acquaintance of his father's who has been helping with his secret plans. Or perhaps he'll come across a captive who was being held by his father for some unknown reason.
One possible plotline could be that Adrien's father is facing a financial crisis, and Adrien uses his intelligence and charm to attract investors or find new business opportunities. Another could be that his father is ill, and Adrien takes on more responsibilities at home and in his father's business to keep things running smoothly.
Well, one possible plot could be that Adrien is initially very conflicted about seeing his father in prison. He might be angry at his father for the things he's done that led to his incarceration, but also still have some lingering love or sense of family obligation. As he visits, his father could try to manipulate him into believing he's innocent or try to get Adrien to do something on the outside for him. Adrien would then have to struggle with whether to trust his father or not and figure out how this visit will impact his own life and his relationships with others.
It's possible that when Adrien joins his father, they embark on an adventure together. They could explore a mysterious place or solve a family mystery. Along the way, Adrien would learn more about his family history and heritage, and they would bond over the shared experience.
Well, perhaps in the fanfiction, Adrien visits his father in prison to seek closure. His father could have committed some heinous crime that has affected many people, including Adrien. During the visit, Adrien might find out some secrets about his family that his father has been hiding, which adds more complexity to the story.
Adrien would probably feel a mix of emotions. He'd likely be angry at his father for the wrongdoings that landed him in prison. But at the same time, he might also feel sad because it's still his father.
Maybe Adrien noticed some strange behavior from Nino that seemed similar to what he imagined Hawkmoth would do in fanfiction.