In such a fanfic, Anakin would probably be a very protective father. He knows the power his children possess, so he'd be cautious. He might start their training early, but also let them have a normal childhood. For example, they could go fishing on Naboo or explore the forests of Endor. He'd be there to guide them through their Force - related experiences, and help them understand the light and dark sides within themselves.
His past would be a huge influence. Anakin's fall to the dark side and his experiences would make him extremely cautious. He'd be determined not to let his children go down the same path. So he might be strict about their use of the Force at times. But also, his love for Padmé would make him want to give them a loving and warm family environment.
One possible fanfic could be about Anakin using time travel to prevent the fall of the Jedi Order and save Padame. He could then ensure a better future for Luke and Leia, guiding them in the ways of the Force without the dark shadow of the Empire looming over them.
The fanfic could explore family dynamics through the eyes of Luke and Leia growing up without their real parents. How they unknowingly carried certain traits of Anakin and Padame. For instance, Luke's strong connection to the Force like his father, and Leia's leadership skills which could be seen as something she inherited from Padame. Then, when they discover the truth about their parents, it causes a shift in their relationships with each other and with the memories of their parents.
In this kind of fanfic, a lot could happen. Maybe Anakin could use time travel to prevent his fall to the dark side. He might go back and make different choices, which would then change the entire future for Luke and Leia. Padme could also be involved in this time - traveling adventure. For example, she could use her knowledge of future events to try and save the Republic in a more effective way. And Luke and Leia, they might end up traveling through time as well to learn more about their parents' past and the history of the Jedi and Sith.
One idea could be a story that focuses on Anakin and Padame's relationship before the events that led to his fall. It could explore their secret meetings and how they coped with the Jedi Code restrictions. Then, as the story progresses, it could show how their relationship influenced Luke and Leia's upbringing and destinies in a more in - depth way than what we saw in the movies. For example, Padame could have left some hidden teachings or messages for her children that they discover later in life.
Perhaps a fanfic that delves into the time when Anakin was on the cusp of turning to the dark side. Padme could sense the change in him and tries to prevent it with the help of Luke and Leia from the future who somehow travel back in time. This would create a complex web of relationships and a race against time to save Anakin from the dark side.
One idea could be a story that focuses on Anakin's internal struggle between his love for Padme and his fall to the dark side as Darth Vader, while Luke and Leia unknowingly grow up in the shadow of their father's actions. It could explore how their lives might have been different if Anakin had not turned, and how they eventually come to terms with his true identity.
In a time travel fanfic, Anakin and Padame could be sent forward in time to meet Luke and Leia. At first, they are shocked by the state of the galaxy. But then, they decide to use their knowledge of the past to help Luke and Leia in their fight against the remnants of the Empire. Anakin, having redeemed himself in this new future, could train Luke further, and Padame could offer diplomatic and strategic advice to Leia.
If Darth Vader raised Luke and Leia, Luke could be more introverted. He'd have to constantly grapple with the knowledge of his father's actions and his own potential for darkness. His training would be intense, and he might be less likely to trust others easily. Leia would be a more complex character. She would have a love - hate relationship with Vader. On one hand, he's her father, but on the other, he represents everything she hates about the Empire. This would make her personality more unpredictable, sometimes showing compassion towards Vader and other times being extremely hostile.
A possible plot is a fanfic where Anakin, in his Darth Vader form, has a vision of a different future where he didn't lose Padme. This vision makes him question his loyalty to the dark side. Meanwhile, Luke and Leia are on a mission to rescue their father from the clutches of the Emperor. The story could be filled with emotional reunions and battles between the light and dark forces.