A common plot is characters going back in time to prevent the fall of Cocoon. Another popular one is time travel to save a character who died in the original story.
There are quite a few popular plots in Final Fantasy XIII time travel fanfiction. One is the idea of time - loop scenarios. For example, a character gets stuck in a time loop and has to figure out how to break it while also dealing with the events of Final Fantasy XIII. Another plot involves time travel for the purpose of redemption. A character who made mistakes in the original story goes back in time to make amends. And then there are plots where time travel is a result of some sort of magical experiment gone wrong, and the characters have to deal with the consequences and find their way back to their own time while also changing things for the better in the past.
Noctis is often very popular. His complex personality and his role as the main character in the original concept make him a central figure in many fanfictions. Writers like to explore his internal struggles, his relationships with other characters, and his journey in different ways.
Another plot could revolve around an alternate ending. Instead of the events that were perhaps expected to occur in the game, the fanfiction could take a different turn. For instance, if a character was supposed to die in the game, in the fanfiction they could survive and have a whole new role to play, leading to a completely different story arc for all the characters involved.
One good place to find Final Fantasy XIII time travel fanfiction is on fanfiction.net. There are numerous stories there with various takes on time travel within the Final Fantasy XIII universe. Another option could be Archive of Our Own (AO3), which also has a wide selection of fan - created content.
Another common plot is Konohamaru accidentally traveling to a time when the ninja world is on the brink of destruction. He then has to use his skills and knowledge from his own time to try and prevent the catastrophe. This often involves him teaming up with ninjas from that era, some of whom might be initially suspicious of him.
A common plot is that Jon and Sansa travel back in time to change the events that led to the downfall of their family. They use their knowledge of the future to try and prevent tragedies. For example, they might stop Ned Stark's execution. Another popular plot is that they travel to a different time period in Westeros' history and get involved in the events there, like during the time of Aegon the Conqueror.
Another popular plot is time travel for the purpose of learning a long - lost magic. A character might travel to a time when a particular powerful magic was still known and try to bring that knowledge back to their own time. This can involve adventures in ancient magical libraries or encounters with long - dead witches and wizards who were masters of that magic. It also often has the character facing various challenges and obstacles along the way, like dealing with guardians of the ancient knowledge or rival time - traveling witches who want the magic for themselves.
One popular plot is Rose Weasley traveling to the past to meet her parents when they were students. She gets to see how they fell in love and all the challenges they faced. It's a heartwarming plot as she gets to understand her parents better.
In some fanfictions, Sasuke time traveling and meeting Naruko leads to a romantic plot. Since he has the knowledge of the future, he might see Naruko in a new light. He could be more open to her feelings and they might start a relationship earlier than in the original story. For example, he could go back to a time when they were on a mission together and instead of being cold towards her, he starts to show his affection. Another idea is that Sasuke travels to a time when Naruko is at her lowest point, like after the death of someone important. He then uses his future knowledge to comfort her and help her become stronger, which then blossoms into a deeper connection between them.
Another common plot involves Damian traveling to the future. He might see a dystopian version of Gotham or the world where the Bat - family has failed in some way. Then he has to figure out how to change the present to avoid that future. For instance, he could discover that Batman has turned evil in the future and has to find a way to stop that from happening in his own time. Well, in this kind of plot, there are often a lot of emotional moments as Damian grapples with the knowledge of what could be. He may also meet future versions of his family members who are very different from what he knows, which adds to the complexity and drama of the story.
One common plot is going back to prevent a major disaster. For example, they might go back to stop the Uchiha massacre. This gives them a chance to change the future of the ninja world.