One common theme could be the clash of different personalities. Aya is from the 'mad father' universe with her own set of characteristics, and Dio has his very distinct personality. Their interaction can lead to themes of power struggle or mutual discovery.
There are a lot of fanfiction out there, but it's not easy to point out particular 'mad father aya x dio fanfiction' right away. You can use search engines and type in specific keywords like 'aya and dio from mad father fanfiction'. Another option is to ask in fan groups dedicated to 'mad father' or to the broader fandom that might be interested in this kind of crossover. It's possible that other fans have already found some great reads and can recommend them to you.
For Dio, you can start by exploring his backstory more. Maybe he has a tragic past that led him to be in the situation with the mad father. This can explain his motives and actions. As for Aya, focus on her emotions. She could be a very empathetic character, which can be shown through her reactions to the other characters' pain.
One common theme could be the exploration of the relationship between Aya and Dio. It might involve how their different personalities interact, like Aya's innocence or determination clashing with Dio's more complex and often villainous nature.
One common theme might be adventure. Since 'Mad Father' has an interesting and somewhat dark world, in fanfics, Dio and Aya could embark on adventures within that world.
One idea could be that Dio and Aya are forced to team up to escape the horrors of the mad father's mansion. They start off distrusting each other but gradually learn to rely on one another.
I'm sorry, I don't have a specific 'mad father aya x dio fanfic' to recommend directly. You can try searching on some fanfiction websites like Archive of Our Own (AO3). There might be various works created by fans that combine these two elements.
There are many fanfics out there, but for 'mad father dio x aya fanfic' specifically, you could also use search engines. Just type in the exact phrase. However, be prepared that not all results might be of high quality. You may need to read through a few to find the ones that really interest you. Fanfic quality can vary greatly depending on the writer's skill and interpretation of the characters.
One common theme could be the exploration of their relationship. It might show how they interact, support or conflict with each other. Another could be adventure, where they go on some sort of journey together in the story.
It could be the Mad Father himself. If he were to find out about the Miraculous and try to use them for his own twisted experiments, he would make a great antagonist. He could try to capture Ladybug and Chat Noir to study their powers.