Naruto and Minato could have adventures in the spirit world together if they were the same age in fanfiction. They could face powerful spirits and learn spiritual ninja techniques. Their combined courage and determination would help them overcome the challenges there. They might also meet the previous Hokages in the spirit world and get some unique training or advice, which would be very beneficial for their growth as ninjas.
They could go on a mission to find a lost pet in the village. Since they are the same age, they would have similar levels of energy and curiosity. Naruto's determination and Hana's skills with animals might combine well to track down the pet and return it to its owner.
They could go on a mission together to retrieve a lost ninja art scroll. Since they are the same age, they might have a competitive yet friendly relationship during the mission, constantly trying to outdo each other in combat skills but also having each other's backs.
They could go on adventures to discover ancient ninja secrets. Since they are the same age, they might team up to explore hidden places that are said to hold great power or knowledge. Maybe they would search for lost jutsu together and face various challenges along the way.
Well, they might embark on a journey to find a rare herb that has the power to heal any injury. Shizune's medical knowledge would be crucial in identifying the herb, and Naruto's strength and determination would keep them safe from any threats along the way. They could also get into all sorts of scrapes with other ninja clans who also want the herb for their own purposes.
They could have training adventures together. Since they are the same age, they might compete in various ninja skills, like who can master a new jutsu faster. Maybe they'd go on missions side by side, facing challenges and relying on each other's unique abilities.
They could have all sorts of adventures. For example, Minato and Kushina could train Naruto together, passing on their unique jutsu. They might go on missions as a family, facing powerful enemies. Minato's Flying Raijin could be combined with Kushina's chakra chains in battle strategies. And Naruto would grow up with the love and guidance of both his parents, becoming an even more powerful ninja at a faster pace.
One possible plot could be that Naruto, being the same age as Minato, is trained directly by Minato from the start. Minato could pass on all his skills and knowledge without the need for other mentors like Jiraiya or Kakashi. They could face the threats to the village together much earlier, and Naruto might grow up with a different sense of confidence and leadership, having his father by his side all along.
A plot twist could be that with Naruto at the same age as Minato, the Nine - Tailed Fox attack on the village might play out very differently. Naruto, already having his own strong will and the potential of a jinchuriki, could team up with Minato to fight off the fox in a different way. Maybe they find a way to seal the fox without sacrificing Minato, which would completely change the future of the Hidden Leaf Village. It could also mean that Naruto grows up with both his parents, leading to a much more stable and perhaps different - natured Naruto, less lonely and more confident from the start.
Well, if Naruto and Minato were the same age in fanfiction, the whole dynamic of the story would be completely different. For one thing, Minato wouldn't be Naruto's father. This would mean Naruto might not have the Kyuubi sealed within him in the same way. Also, their relationship could be more of a friendly rivalry. Without the father - son bond, Naruto might have to find his own path in a more independent way, and Minato could be seen as a peer rather than a role model or a figure of authority.
They could embark on a journey to stop a powerful dark force that was unknown in Minato's time. Naruto, with his future knowledge, could lead the way and show Team Minato new ways to fight.