Maybe Ash's old Pokémon have unique skills that are rare in Kalos. So, he uses them to gain an advantage in Pokémon contests or battles. His Charizard, for instance, could be a formidable opponent against Kalos's dragon - type Pokémon, and this could lead to some exciting rivalries and plot twists.
Perhaps there is a threat to Sinnoh that only Ash's old Pokémon can help solve. Some kind of ancient evil that has knowledge of Ash's past Pokémon battles. Ash and his old Pokémon then have to work together to defeat this threat. They might need to combine their old strategies with new ones they learn in Sinnoh to succeed. And along the way, Ash might meet some of his old friends who are also in Sinnoh and they help him in his mission.
It could be Pikachu. Since Pikachu has been with Ash from the very beginning and is his most iconic Pokémon. It's very likely that in Sinnoh fanfiction, Pikachu would be frequently used as it has a strong bond with Ash and is also very powerful.
Well, it could mean that Ash is getting inspiration from the creativity in those old fanfics. Maybe he finds unique storylines or character interpretations that he can use in his own Pokemon journey, like new strategies or ways of bonding with his Pokemon.
It could be for nostalgia. Ash has a long history with his Pokémon, and using the old ones in a Unova fanfic might be a way to bring back memories for the readers who have followed his journey from the start. It also shows his growth as a trainer, as he can rely on the skills and bonds he's developed with his older Pokémon in a new region.
It could also expand the lore. Old fanfics often have their own interpretations of the Pokemon world. When Ash uses ideas from them, it might introduce new concepts or relationships that weren't part of the original story. This can make the Pokemon world seem even larger and more complex.
You can start by looking on fanfiction.net. It has a large collection of Pokemon fanfics, and you're likely to find quite a few 'ash old pokemon fanfic' there. Just use the search bar and type in relevant keywords.
Some 'ash old pokemon fanfic' take a different turn and explore what would have happened if Ash had made different choices. For instance, if he had chosen a different starter pokemon instead of Pikachu. This kind of fanfic can be really exciting as it rewrites the whole pokemon journey in a new and unexpected way.
Typically, his old team could include Pikachu, of course. Then there might be Charizard, Bulbasaur, Squirtle, and others like Greninja. These Pokémon have been with Ash through different adventures in various regions.
Maybe Tracey. He was also an acquaintance of Ash. Since Tracey has his own unique skills and knowledge about Pokemon, his presence could bring new elements to the story. He could help Ash and other friends with things like Pokemon research or understanding some rare Pokemon behaviors.