In this fanfiction, Minato could show his protectiveness in a very direct way. Maybe he has some kind of special connection with Naruto that allows him to sense Naruto's distress from the afterlife. So when Naruto is in a fight or in a dangerous situation, Minato's spirit could manifest itself and directly interfere with the situation to keep Naruto safe. He could also have left behind some sort of guardian entity or power within Naruto that would take over and protect Naruto when he is unable to defend himself.
Well, in the fanfiction, Minato could be protective by influencing Naruto's teachers or the people around him. He might use some kind of spiritual communication to tell them to look after Naruto carefully. For instance, he could appear in Iruka's dreams and ask him to be extra vigilant about Naruto's safety. And also, Minato could have set up some sort of pre - arranged protection plan in the village that is specifically for Naruto, so that whenever Naruto is in trouble, the village mechanisms would automatically be more inclined to protect him.
Minato might show his protectiveness by always being near Naruto in spirit. For example, he could leave behind some kind of jutsu or power that activates when Naruto is in great danger, like a hidden seal that releases a powerful defense.
One touching moment could be when Minato's spirit appears right in front of Naruto when he is on the verge of being defeated by a powerful enemy. Just seeing his father's figure gives Naruto new strength and hope, which shows Minato's protectiveness in a very emotional way.
She might physically stand in harm's way. For example, if there's a threat approaching Naruto, Kushina would put herself between Naruto and the danger. Just like how a mother bear protects her cub.
He uses his skills as a ninja to protect Naruto. He sets up special seals around Naruto's crib to keep out any potential threats. Also, Minato might try to use his chakra to boost Naruto's weak body. He would transfer his own life force a little bit at a time to help Naruto fight the sickness, which is a huge sign of his love.
In fanfiction, Minato's possessiveness might show in his reactions to Naruto's achievements. He could take too much pride in Naruto's success as if it's only his to be proud of. For instance, when Naruto accomplishes something great, Minato might act as if he's the sole reason for Naruto's success and not give enough credit to Naruto's own hard work and the influence of his friends.
In many such fanfics, Percy uses his intelligence. For example, he might study the laws and regulations of the wizarding world thoroughly to find loopholes that can protect Harry from unjust punishments or accusations.
Often, in such fanfiction, Itachi protects Naruto from the Akatsuki. Since Naruto is the jinchuriki of the Nine - Tails, the Akatsuki might target him. Itachi, being part of the Akatsuki but having his own motives, would ensure Naruto's safety from his comrades. He could mislead them about Naruto's whereabouts or lie about Naruto's power level to keep them from making a hasty move against him. Itachi might also protect Naruto from the villagers' negative attitudes. Naruto was often ostracized in the village, and Itachi could use his influence or just his presence to make the villagers think twice before treating Naruto badly.
Another way would be through his actions. For example, if the villagers were being unjust to Naruto, he might start by protecting Naruto more visibly. He could also limit his assistance to the village in other areas until they corrected their behavior. This would be a clear sign of his anger and dissatisfaction with the villagers.
In some fanfictions, Minato saves Naruto physically. For example, he might use his teleportation jutsu to appear right in the middle of a fight and whisk Naruto away from danger. In others, he could save Naruto spiritually. He might enter Naruto's mind, like in the fanfic 'Minato's Mind - Saving Mission', and give him the strength and confidence to overcome his inner demons. Sometimes, Minato saves Naruto from a political situation. For instance, in 'Minato and the Hidden Leaf's Politics', he uses his influence and wisdom to protect Naruto from being used as a political pawn.
Well, in some fanfictions, Minato might use his powerful jutsu to break through the barriers between the living and the dead and directly reach Naruto. He could also try to influence the people around Naruto to bring him closer to where Minato is, like using his spirit to communicate with Naruto's friends and convince them to help.
Minato's presence can have a huge impact. He can act as a mentor, teaching Naruto things he never knew about his family and heritage. His wisdom and skills can inspire Naruto to reach new heights in his training and ninja development.