His magic could be related to his chakra control. Maybe he could turn his chakra into different elements of magic, like fire magic similar to his Fireball Jutsu but with a more magical twist. For example, instead of just a normal fireball, it could be a fireball with runes inscribed on it for extra power.
Given Naruto's connection to the Nine - Tails, his magic might also be influenced by it. He could have a unique form of magic that taps into the Nine - Tails' power. It could be something like a berserk mode where his magic power skyrockets, but he has less control. Or he could use the Nine - Tails' chakra to perform extremely powerful and forbidden magic spells that are normally beyond his capabilities.
Jiraiya could be a possible teacher. He's always been Naruto's mentor in the original series. In this fanfiction, he could have some knowledge of magic and teach Naruto the basics. He could show Naruto how to combine his existing ninja skills with magic, like using magic to enhance his Rasengan.
His rule would probably be fair. Naruto has always been about justice and understanding. He might reform the hell system, making it less cruel and more about rehabilitation for souls.
If Naruto becomes a Joker fan in the fanfiction, his new look could be really different. He would probably ditch his orange jumpsuit for something more in line with the Joker's style. A long, tattered purple coat perhaps, with some dark makeup around his eyes to give him that menacing look. His shoes could be replaced with some clown - like shoes, and he might carry around a few 'joker - ish' accessories like a deck of cards or a fake flower that sprays water. His overall appearance would be a blend of his ninja - like physique and the Joker's flamboyant and chaotic style.
His teaching style might be very hands - on. Naruto is someone who has learned through experience, so he would likely encourage his students to do the same. He would probably tell them stories from his own adventures to make lessons more interesting.
If Naruto becomes like Hashirama in fanfiction, it could mean he has a similar leadership style. Hashirama was known for his charisma and ability to bring people together. Naruto already has those qualities, but it could be enhanced. He could also inherit Hashirama's skills in wood - style jutsu, which would give him a whole new set of abilities in combat and for building things in the village.
In such a fanfiction, Naruto might become a dark and brooding figure. His usual positive traits could be twisted. Maybe he has nightmares that change his perception of the ninja world, leading him to question everything he once believed in. This could result in him having a more cynical view and taking actions that are out of character for the original Naruto, like being more ruthless in battle or distrusting his friends.
The plot could involve Naruto using his ninja skills in the world of exorcism. He might use his shadow clone jutsu to outnumber demons. For example, he could send clones to different areas to search for and fight demons while he focuses on the stronger ones. His Rasengan could be modified to have an exorcising effect, perhaps by infusing it with spiritual energy.
In this kind of fanfiction, Naruto might gain god - like powers such as the ability to manipulate time and space. He could use these powers to prevent wars and bring eternal peace to the ninja world.
In a fanfiction where Naruto becomes a lord, he might use his ninja skills for ruling. He could ensure the safety of his land with his combat abilities. Also, he'd probably bring his values of friendship and perseverance to governance, making his territory a place full of unity and hope.
In such a fanfiction, Naruto might adopt Kakashi's laid - back attitude. He could start reading those 'adult' books Kakashi likes in his free time, and also become more of a lone wolf in his missions, relying more on his own skills like Kakashi does.