Dark Vader, also known as Darth Vader, was originally Anakin Skywalker. He was a Jedi with great potential. However, his fear of losing his loved ones, especially his mother's death and his premonitions about Padmé, led him to be seduced by the dark side of the Force. Palpatine manipulated him, and in a fit of rage and desperation, Anakin turned against the Jedi Order.
Darth Vader was originally Anakin Skywalker. He was a slave on Tatooine. Qui - Gon Jinn discovered his strong connection to the Force and took him for Jedi training. Anakin had great potential but was haunted by fear, especially of losing his loved ones. His relationship with Padmé Amidala led to his downfall. He turned to the dark side under the influence of Palpatine, who promised him the power to save Padmé. After a fierce battle with Obi - Wan Kenobi, he was severely injured and transformed into Darth Vader, becoming a powerful enforcer for the Galactic Empire.
Well, first, Anakin was found on Tatooine as a slave boy with a strong Force connection. Then, his training as a Jedi, which was filled with both successes and doubts from the Jedi Council. His mother's death was a huge turning point, leading to his first real taste of the dark side. His relationship with Padmé and his desperation to keep her alive ultimately led him to Palpatine's side, where he fully embraced the dark side and became Darth Vader. His subsequent battles and his role in the Empire are also important parts of his back story.
In such a fanfiction, Darth Vader might try to prevent his fall to the dark side. He could use his knowledge of the future to avoid the events that led him to become a Sith. For example, he might prevent the death of his mother or his duel with Obi - Wan on Mustafar.
Well, Anakin Skywalker was a young and talented Jedi. He had a difficult childhood as a slave, which made him very attached to those he loved. His mother's death was a huge turning point. It filled him with anger and hatred. And then, his relationship with Padmé was a secret, which added to his inner conflict. The Jedi Council's actions towards him, like not making him a Master, made him feel unappreciated. All these factors combined led him to turn to the dark side and become Dark Vader.
In such a fanfiction, Darth Vader could change the course of history. He might prevent the rise of the Empire or alter his own fall to the dark side. For example, he could warn Anakin Skywalker about Palpatine's true intentions, thus changing the entire Star Wars timeline.
His presence could change the power balance. If he sides with the Jedi, the Sith would be at a disadvantage. The Sith rely on secrecy and manipulation, but with Darth Vader knowing their plans, they would be exposed more easily.
He could meet his younger self, Anakin Skywalker. That would be a really interesting encounter. He might also meet Qui - Gon Jinn, who could sense the conflict within him. And there's a chance he'd cross paths with Yoda in his prime, which would lead to some intense confrontations or perhaps even unexpected alliances.
Well, in a 'Darth Vader goes back to the Clone Wars' fanfiction, he might seek to alter the relationships within the Jedi Order. He could try to influence Anakin Skywalker (his former self) in a different way. For example, he could try to expose the Sith plot earlier, which would completely change the dynamics of the Clone Wars. He might also try to use his advanced combat skills and knowledge of the dark side to turn the tide of certain battles in a different direction than what originally happened.
A great plot twist could be that Darth Vader travels back to the time when the Jedi Order was at its peak. His dark side presence is detected by the Jedi Council immediately. However, instead of being able to simply capture or kill him, they find that his knowledge of future events gives him an edge. He might use this to manipulate the Jedi, creating internal strife within the Order. This could also lead to some Jedi being tempted by the dark side because of the power that Vader represents. And all of this could ultimately reshape the future of the galaxy far more than anyone expected.