Well, in the fanfiction about Voldemort's memories, there could be revelations about his relationships. For example, his connection with his mother, Merope Gaunt. His memories might also show his first encounters with the idea of immortality and how he started to plan his Horcruxes. It can give a deeper understanding of his motives.
Harry might become more cynical. Since Voldemort has seen a lot of dark and cruel things, those memories could taint Harry's view of the wizarding world. He could start to question the motives of people around him more, even those he once trusted, like Dumbledore.
One possible implication is that Harry would gain a deep understanding of Voldemort's motives. He might see how Voldemort's past traumas, like being an orphan and feeling rejected at Hogwarts, led him down the dark path. This could make Harry more empathetic in a strange way, or it could also be a huge burden on him as he has to deal with all the dark and twisted thoughts that Voldemort had.
We can expect to see his early days at Hogwarts. Perhaps there are memories of him being bullied or feeling superior to others. This can explain how his personality developed over time.
He might become more isolated. As his friends might not fully understand what he's going through with these new memories, Harry could start to pull away from them. This would force him to become more self - reliant and introspective. He'd have to dig deep into his own identity to separate himself from Voldemort's influence, which would lead to a more complex and mature Harry.
In the original story, Voldemort doesn't have access to Harry's memories in this way. So in the fanfiction, it creates a completely new scenario. It allows for a different kind of exploration of their relationship. Instead of just their physical and magical battles, we get to see a more psychological interaction.
Well, in such fanfiction, it's fascinating to consider how Voldemort's view of Harry might shift. He might see Harry's memories of facing challenges and growing stronger through them. This could either make Voldemort more determined to defeat Harry as he realizes his strength, or it could potentially make him more hesitant as he sees the full scope of Harry's experiences.
Harry could become more powerful in a way that scares his friends. Voldemort's training might focus on the Dark Arts, which are powerful but dangerous. This could change Harry's magic style. He may become more solitary as his new skills and knowledge set him apart from his Hogwarts friends who follow a more traditional path of magic.
One interesting plot point could be that Harry discovers a hidden agenda of Voldemort that was unknown to everyone. Maybe there was a part of Voldemort's plan that was so well - hidden that only by having his memories can Harry find out. This could lead to a new race against time to stop something that Voldemort had set in motion long ago.
Yes, there are some fanfictions exploring such a wild and unorthodox concept. Fanfiction often takes creative liberties and twists the original story in unique ways. However, this goes completely against the established canon of the 'Harry Potter' series.