Well, one way could be that Naruto, being the son of Hades, would have unique powers. He might be able to use his shadow clones in a new way, like sending them into the Underworld to gather information. His connection to Hades could also make him a target for other gods or demigods who are either afraid of Hades' power or want to use Naruto for their own gains. Maybe he would struggle to fit in at Camp Half - Blood at first because of his different origin compared to the normal demigods there.
The story could start with Naruto being discovered in the Percy Jackson world. Since he's the son of Hades, he might have an instant connection with the dead. He could use this to his advantage, like communicating with the spirits of past heroes to gain wisdom. However, his Naruto - like personality of never giving up and being extremely determined might clash with the more traditional ways of the demigods. He could introduce new fighting styles, like his ninja techniques, which would be a huge shock to the demigods who are used to their own combat methods.
One way to develop the storyline could be to explore Percy's struggle with his new identity. Since Hades and Persephone are such complex deities, Percy might have a darker side to him. He could struggle with controlling powers related to the Underworld, like shadow manipulation or communicating with the dead. For example, in a school setting, he might accidentally let out some spooky manifestations when he's stressed.
The main antagonist could also be an ancient and powerful spirit from the underworld that was sealed away long ago. Percy's presence as the son of Hades accidentally awakens this spirit. The spirit then starts to spread darkness and despair throughout the world of the demigods, and Percy has to find a way to stop it before it's too late.
Another option could be some rogue demigods who are jealous of the son of Hades' powers. They might form a group and try to cause trouble for him and Percy Jackson. They could be working with some minor gods who have a grudge against Hades, creating a complex web of enemies.
Hades' character could be developed by showing his more paternal side towards Percy. He might start as a cold and distant figure but gradually show concern and protectiveness. For example, he could save Percy from a dangerous monster in the Underworld.
Percy could be developed by showing his confusion at first. He's used to being a son of Poseidon, so being a son of Khione throws him off. He might struggle with learning new powers and how to use them effectively. For example, he accidentally freezes his own feet when he tries to use ice powers for the first time.
Naruto, as the son of Hades, would have some really cool powers. His Rasengan could potentially be infused with the power of the Underworld, making it a much more deadly attack. He could also have the power of persuasion over the dead, which means he could make them tell him secrets or do his bidding. His ability to sense chakra in the Naruto world could be translated into sensing the life force or the 'essence' of beings in the Percy Jackson world. This would give him an edge in detecting enemies, whether they are living or undead.
You can start by giving her a distinct personality. Maybe she's shy because she's always been feared for her father's sake. Then, gradually show her growing confidence as she discovers her own strengths. For example, if she has the power to raise small skeletons as minions, at first she's scared of it, but later she learns to use it for good. Also, explore her relationships with other characters. Her friendship with Percy could be based on mutual understanding of being different among the demigods.
You could also develop his character by showing his interactions with other gods and goddesses. As the son of Hecate, he might attract the attention of some deities who either want to help or hinder him. His reactions to their offers and threats would shape his character. For example, if a god offers him more power but at a great cost, how does Percy respond? Does he accept the power out of desperation or does he hold true to his values? This would show his growth and development.
One possible plot could be Percy struggling with the duality of his parentage. He might face discrimination from both the children of Hades and Poseidon. For example, the children of Poseidon could see him as a threat because of his connection to Hades, and vice versa. He could then go on a journey to prove that his dual heritage doesn't define him, but rather gives him unique powers to protect the world of the gods and mortals.
Their relationship could start with Percy seeking refuge at one of Hestia's hearths during a difficult time. Hestia, being the gentle goddess she is, offers him comfort and wisdom. This initial encounter could be the foundation for a deeper bond as Percy starts to see Hestia as a motherly figure, much like how he saw Sally Jackson.