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.
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.
He might use them because they are his tried and true companions. Ash has a strong bond with his old Pokémon, and in the Kalos region, he wants that familiar support.
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.
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.
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.
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.
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.