Perhaps she is half - vampire herself. This would create a lot of internal conflict as she tries to balance her human side and her vampire instincts. She could also be in a love triangle with a vampire and a human, which would add a lot of drama to the story.
One possible story could be that Kaien Cross's daughter discovers she has unique powers in the world of Vampire Knight. She might struggle to fit in among the vampires and humans, while also trying to understand her father's past and his connection to the vampire world.
She could be a rebel. She might oppose the traditional ways of the vampire hunters or the vampires. For example, if she falls in love with a vampire when she is supposed to be a hunter, it would create a great conflict. This could lead to her being ostracized by her own group and having to find her own path.
In a fanfiction, Kaien's daughter might be a key figure in bringing about a truce between the vampires and the vampire hunters. She could grow up with a deep understanding of both sides, having been exposed to the vampire world through her father's connection and the hunter world through her family's legacy. This would lead to her trying to bridge the gap between the two groups, facing many challenges along the way.
She could be kidnapped by a group of rogue vampires who think they can use her to gain leverage over the headmaster. Her friends, both human and vampire, would then have to team up to rescue her. During her captivity, she might learn some secrets about the vampires that could change the way she views them.
The plot could revolve around her discovery of her family's past. As she uncovers the secrets and the struggles her parents went through, she gains a new understanding of herself and her place in the world. For instance, she might find old diaries or hear stories from the elders that open her eyes to the sacrifices her parents made for the greater good.
The plot could revolve around a rivalry at first. Hiruzen's daughter might see Minato as a competitor in the ninja academy. But as they get involved in team battles and joint missions, they begin to respect each other's skills. Eventually, this respect turns into admiration and then love. They could face difficulties like other ninjas being jealous of their relationship or the village elders having concerns about their union.
One possible fanfiction could be that the headmaster's daughter discovers a hidden power within herself. Maybe she has the ability to control a special type of vampire energy that no one knew about. This power could put her in a dangerous position as different vampire factions might want to use her for their own gain.
In Vampire Knight fanfiction, Rido's daughter could play a villainous role. Since Rido was a rather malevolent character, she might follow in his footsteps and cause chaos among the vampires and humans. She could be seeking revenge for her father's death or trying to fulfill his unaccomplished plans of domination.
One possible plot could be that the vampires from Vampire Knight are suddenly transported to the real world. They would have to deal with modern technology and society while trying to hide their true nature. For example, they might struggle with using cell phones or getting around in cars. And they would have to be extra careful not to expose their fangs or their need for blood in public.
Perhaps in the fanfiction, Hedwig is lost near King's Cross Station. Snape, who is there for some mysterious reason, decides to help find Hedwig. As he searches, he starts to understand the significance of Hedwig to Harry and through this, his view of Harry softens a bit. It could be a story about unexpected connections and growth in Snape's character.