Seeing Naruto's power in fanfiction can greatly influence Boruto's character. It could make him more determined to reach his father's level. He might start training harder and be more serious about his ninja duties.
One common scenario is Boruto getting to see Naruto in a super intense battle, showing off his amazing jutsu. Another could be Naruto using his power to protect the village, and Boruto watches in awe.
Boruto might be in awe. He has always known his father as the Hokage, a powerful and respected figure. Seeing Naruto's past full of struggles, loneliness, and determination would make him realize how far his father has come. It could also make Boruto more empathetic towards Naruto and perhaps inspire him to be more like his father in some ways.
It could also be that Naruto sees in Boruto's eye a sign of an emerging danger. The eye might hold a clue to a new enemy or a brewing conflict. Naruto, being the experienced ninja he is, would then start to take precautions and train Boruto more intensively to face whatever this sign in his eye indicates.
Well, Naruto could show Boruto his Sage Mode power. Sage Mode gives Naruto enhanced strength, speed, and the ability to sense chakra more acutely. It's a very powerful form that Naruto has mastered over time. By revealing it to Boruto, he might be teaching Boruto about the different levels of power and the hard work required to achieve such power.
Probably his time at the Ninja Academy. Naruto was always getting into trouble there, but it was also where he made some of his first friends. Also, his encounters with the Third Hokage could be shown. The Third Hokage was like a grandfather figure to Naruto, and their interactions were important in Naruto's development.
Maybe it's the high expectations that Naruto has for Boruto. Naruto is a hero, and he might unknowingly put a lot of pressure on Boruto to follow in his footsteps. Boruto could be scared of not being able to meet those expectations.
In a 'naruto dies boruto fanfic', Boruto's character would go through a major transformation. He would be forced to grow up overnight. Initially, he might be consumed by anger and a desire for revenge if Naruto was killed unjustly. But as time passes, he would learn to channel that energy into positive change. He would study his father's leadership style and try to implement it in his own way. He would become more diplomatic, forging alliances with other villages to strengthen Konoha's position. His sense of justice would be refined, and he would be more committed to protecting the world his father loved so much.