First, start with their existing personalities. Yumi is often serious and focused, while William can be a bit brash. Have them interact in situations that force them to understand each other better. For example, in a group mission on Lyoko, they might have different ideas on how to approach a problem. By working through these differences, their relationship can start to grow.
Perhaps the fanfiction focuses on the cultural clash between the two groups. The Persona 4 characters are from a small town, while the Persona 5 crew is from the big city. Their different ways of handling things and their unique Personas could lead to some interesting interactions. For example, Yu and Joker might have different leadership styles that they have to reconcile in order to succeed against the shadows.
One idea could be a story where William, after being rescued from XANA's control, has trouble fitting back into normal life at Kadic. Yumi could be the one to help him through it, and during this process, they discover new feelings for each other. Maybe they have to face some remnants of XANA's influence together, which makes their bond stronger.
Another way their relationship could develop is if Yumi has a personal goal, like finding her long - lost family. Naruto, being the kind - hearted person he is, decides to help her. During this journey, they face many obstacles and challenges. Through these difficulties, they form a strong bond. They might argue at times, but they always come back to support each other, and this cycle of conflict and resolution helps their relationship to grow and evolve.
Highschool DxD has a rich world - building, and when it comes to Yumi fanfiction, writers can play with the existing lore. They can create new adventures for Yumi within the context of the Highschool DxD universe. Maybe she gets involved in a secret mission or discovers a new power, which makes the fanfiction really engaging.
Growth and self - discovery are other themes. The relationship between the two can be a catalyst for each character to learn more about themselves, as they interact and face different situations together in the fanfic stories.