Perhaps in the fanfiction, Peter has to deal with the loss of Natasha in a unique way. Since she is his mother, her death (assuming it occurs in the story's timeline) would hit him hard. He could then take on her mantle in a more emotional and personal way. He might use his powers (if he has any like in the Spider - Man universe) to continue Natasha's work in protecting the innocent, while also dealing with his grief and trying to live up to her name.
The plot could involve Peter trying to uncover his mother's past. Since Natasha has a complex history, Peter might be curious about it. He could start investigating the Red Room and the things Natasha went through. This could lead to him facing some of the same threats and enemies that Natasha once did, and he'd have to use his own skills, which were influenced by Natasha, to overcome them.
One possible plot could be that Peter grows up with Natasha's skills and values. He might be trained by her in combat and espionage. For example, he could learn how to use different weapons and how to deceive enemies just like Natasha. Maybe they go on secret missions together, with Peter gradually proving himself as a worthy heir to Natasha's abilities.
Perhaps the story could explore the relationship between Peter and the other Avengers. Since Bucky has his own history with the team, Peter might face some acceptance issues at first. But as he proves himself, he becomes an integral part of the group. He could also inherit Bucky's past traumas in some way and have to deal with them while still being a hero.
Well, one possible plot could be Peter growing up in Asgard. Maybe he has to deal with the expectations of being Loki's son. He might inherit Loki's mischievous nature but also has his own sense of justice, which could lead to conflicts with the more traditional Asgardian values.
One possible plot could be Peter growing up in Asgard, learning the ways of the Asgardians and struggling to control his powers which are a mix of his own and those he might inherit from Thor.
Another theme could be redemption or healing. Bucky has his own troubled past, and Natasha also has a complex history. Having Peter as their son could be a way for them to find a new purpose and heal from their past traumas. The fanfiction might explore how they become better versions of themselves through their relationship with Peter, and in turn, how Peter helps them in this process.
Well, perhaps in the fanfiction, Natasha discovers Peter during one of her undercover missions in Queens. She realizes he's a brilliant but troubled kid with great power. So, she decides to adopt him. Then, she might introduce him to the wider world of international superhero relations. Peter would get to meet other heroes through Natasha's connections, and together they could go on missions that require both Peter's spidey - sense and Natasha's combat skills.
In some fanfictions, Peter son of Natasha might be set in an alternate universe. For example, he could be growing up in a world where the Avengers never formed. This type of fanfiction often explores how his life would be different, and how he would still manage to become a hero with Natasha's influence guiding him.
One possible plot could be Peter growing up in the Stark mansion, having access to all of Tony's technology. He might start inventing things at a very young age. And when he gets his spider - powers, Tony could be more directly involved in helping him develop his suit and his skills as a superhero.
Well, it could be that Peter discovers his true identity as Tony's son through some hidden documents or a revelation by an old acquaintance of Tony's. Maybe he has some special powers that are linked to Tony's technology, and as he uncovers his relation, he also has to face the enemies that were once after Tony.
Peter might be more reserved and calculating like Natasha. Instead of his usual impulsive self as Spider - Man, he would think things through more carefully. His sense of humor might also be a bit darker, influenced by Natasha's past and her own brand of dry humor.
Another option is to join relevant fan communities on social media platforms like Reddit or Tumblr. Fans often share their favorite fanfictions in these communities. In these 'Peter is Bucky and Natasha's son' fanfictions, the story could also delve into how Peter interacts with other characters from the Marvel universe, like Tony Stark or Steve Rogers, considering his new family ties.