It could be Frieza. Frieza has a long - standing grudge against the Saiyans, especially Vegeta. He might kidnap Vegeta to torture him or to use him as a bargaining chip against the other Saiyans. Another possibility is Cell. Cell might see value in Vegeta's genetic material and kidnap him to extract it for his own evolution.
In a 'Vegeta kidnapped' fanfiction, perhaps Vegeta could be kidnapped by an old enemy seeking revenge. This enemy might be from his Saiyan past. They could be using him to draw out Goku, thinking Goku will come to save Vegeta. Vegeta, being proud, would likely struggle against his captors and try to break free on his own at first.
One common theme could be the idea of rescue. Characters from the Dragon Ball universe might come together to save young Vegeta. Another theme could be Vegeta's growth during the ordeal. He might discover new powers or aspects of his personality while kidnapped.
In a fanfiction scenario where Death the Kid is kidnapped, his friends like Black Star and Maka would surely go on a rescue mission. They would face many challenges and enemies along the way. And his OCD about symmetry might even play an interesting role during his captivity, like getting frustrated with the asymmetry of his prison cell.
Some fanfictions explore their friendship. 'A Saiyan Bond' is about how Kid Vegeta and Baby Goku start to respect and care for each other. They begin to understand that they are not so different after all. It's a heartwarming story that shows the potential for friendship between two strong - willed Saiyans.
I'm not aware of specific 'young vegeta kidnapped fanfiction' works. However, you can try searching on fanfiction websites like Archive of Our Own or FanFiction.net. Just be sure to use appropriate filters to find the relevant stories.
Perhaps Kaito Kid kidnaps a fan by mistake. He was aiming for someone else who looked similar, and this fan is just an ordinary person who happened to be in the wrong place at the wrong time. The fan could be really scared at first, but then as they interact with Kaito Kid, they start to see a different side of him. Kaito Kid might then have to figure out how to let the fan go without getting caught himself.
A young journalist who has been writing articles about Kaito Kid and his heists. Kaito Kid kidnaps the journalist to control the narrative. He wants to make sure that the journalist doesn't publish any more information that could give away his next moves or expose his secrets.
One idea could be that Pit is kidnapped and Hades tries to corrupt him. Maybe Hades offers Pit power in exchange for his loyalty. Pit, being the heroic character, resists but has to find a way to escape while also facing the internal struggle of being tempted by such power.
The popularity comes from the contrast between them. Kid Vegeta is often portrayed as more arrogant, while Baby Goku is more innocent. This contrast creates interesting dynamics in the stories.