Maybe it's a deranged fan of one of the Core Four. Somebody who has an unhealthy obsession and thinks that by kidnapping them, they can have a special relationship with their idol. It could be a fan of Archie's football career or Veronica's glamorous lifestyle. They might be living in their own deluded world and believe that the Core Four will come to love them if they keep them hostage.
Another possibility is a group of criminals who have escaped from prison and have a vendetta against Riverdale in general. They see the Core Four as symbols of the town's hope and prosperity and want to crush that. So they kidnap them to send a message to the whole town that no one is safe.
One common plot could be that a mysterious figure from the town's dark past targets the Core Four because they are getting too close to uncovering some long - hidden secrets. For example, they might be on the verge of revealing the truth about a decades - old murder that someone powerful wants to keep buried. Another plot could involve a criminal gang that mistakes the Core Four for someone else who owes them money or has information they want. Maybe they snatch them up thinking they're getting valuable assets but soon realize their mistake, leading to a tense standoff.
It could be Discord. He loves chaos and might think it's fun to kidnap Twilight and see how her friends react. He could also be after her knowledge of magic to cause more mischief in Equestria.
The Black Hood is a likely candidate. Since he has a history of causing trouble in Riverdale, he might kidnap someone to send a message or continue his reign of terror. He could target Cheryl, for example, thinking she's a symbol of the wealthy and corrupt in the town.
I'm not entirely sure specifically as it could be about different things depending on the context. 'Core four' might refer to a set of four main characters in a particular story or franchise, and a 'kidnapping fanfiction' would be a fictional story written by fans where these characters are involved in a kidnapping scenario.
There could also be a group of villains working together to kidnap Sonic. For instance, a combination of Eggman and some of his more powerful robot creations along with a couple of other villains from Sonic's rogues gallery. They might have a grand plan that requires Sonic's capture, like using his power to open a portal to a world full of chaos energy that they can then control.
A jealous rival of Inuyasha might kidnap Kagome. For example, another demon who wants Inuyasha for himself might think that by taking Kagome, he can get Inuyasha to do his bidding. This would create a lot of drama and conflict between Inuyasha and the kidnapper.
I'm afraid I can't recommend any particular 'core four kidnapping fanfiction' directly. However, you can start by looking at the fanfiction communities related to your favorite series that might have a 'core four' of characters. Check the top - rated or most - reviewed stories with the 'kidnapping' theme. You might also ask in relevant online forums where fans discuss and share their favorite fanfictions.
The Joker is a likely kidnapper. He has a history of causing chaos and targeting the Bat - family. He might see kidnapping Batgirl as a way to get back at Batman or just for his own twisted amusement.
In certain fanfictions, a jealous rival of Amy Rose could be the kidnapper. This could be another female character who has feelings for Sonic and sees Amy Rose as a threat. She might think that by getting rid of Amy Rose, she can have Sonic all to herself. Or it could be a character from Amy Rose's past who has some unresolved issues with her and decides to kidnap her to get revenge or make her pay for something that happened a long time ago.
Well, in a lot of fanfictions, demons are likely kidnappers. They might want to use Sam for some dark ritual or to get information about the Winchesters' hunting secrets. Demons have always been a big threat to the Winchesters, so it makes sense for them to be the kidnappers.