Jiraiya is likely to be a popular character. He was Minato's teacher and has a strong influence on Naruto as well. In a time travel fanfiction, he could provide a lot of wisdom and help in the different situations they encounter. Also, Tsunade could be important. Her leadership skills and medical ninjutsu could be very useful when they are in the past, and she has her own history with both Minato and Naruto's family.
There could be Sasuke. Since Sasuke is Naruto's rival and often involved in the same major story arcs, he might play an important role in this fanfiction. His sharingan abilities could interact with Naruto's newfound speed in some interesting ways, either as an ally or an obstacle depending on the plot.
Sakura could be another main character. She might be shocked by Naruto's arrest and start her own investigation. Maybe she teams up with Sasuke, who also has his own complex feelings towards Naruto. Their combined efforts could play an important role in uncovering the truth.
Rin could also be an important character. She could be the one who takes care of baby Naruto's day - to - day needs, like feeding and cleaning. She could also have a special bond with Naruto, perhaps seeing him as a symbol of hope for the future of the village.
The main characters are obviously Naruto and Minato. Naruto is the protagonist of the Naruto series, a young ninja with the Nine - Tails sealed inside him. Minato is Naruto's father, a very powerful ninja known as the Fourth Hokage. In this time - travel fanfiction, their interactions form the core of the story.
If Minato time - travels, it could change a lot. For instance, if he prevents the Nine - Tails attack, Naruto would grow up in a very different environment. He might not be the underdog he was in the original story. Also, if Minato changes things during the Uchiha clan's situation, Sasuke's story would be completely different. Konoha's political situation would also be altered. There would be less animosity between different clans perhaps.
In a Naruto time - travel Minato fanfiction, Minato could be sent to the future. There, he would see how the village has changed, and might be shocked to find out about the Akatsuki and their actions. He could then work with Naruto and the others to fight against the Akatsuki using his unique skills and knowledge of the past. For example, he could teach Naruto some new jutsu that was lost over time.
It would be very close. Naruto has always longed to know his father, so when he travels back in time to meet Minato, they would quickly bond. They'd probably start training together right away.
Kushina could be an important character even though she's dead in the original story. In this fanfic, her spirit or memories could play a role in Naruto's upbringing. For example, Minato could tell Naruto stories about Kushina's feisty personality and her love for the village.
One popular theme is Minato getting to know Naruto in the afterlife. Since Minato died when Naruto was a baby, fanfictions often explore their relationship in a spiritual realm.
Sakura could be a significant character. In the context of Naruto being Minato's son, her relationship with Naruto might change. She could be more in awe of him at first or have different expectations. Also, Sasuke is likely to be a main character. His rivalry with Naruto could take on new dimensions as Naruto has the added legacy of being Minato's son. Their battles and interactions might be more intense and influenced by Naruto's heritage.