I'd recommend a fanfiction where Ash catches Mew during a battle tournament. In this story, Mew enters the tournament secretly, and Ash is the only one who realizes it's Mew. He manages to catch it during the final showdown. The story is full of intense battles and great character development for Ash.
Perhaps Mew and Mewtwo are in a fight against an evil force that threatens the Pokémon world. Ash arrives at the scene and manages to communicate with them. He offers his help and through their combined efforts, they defeat the evil. As a result, Mew and Mewtwo see Ash as a true hero and allow him to catch them, leading to a new chapter in Ash's Pokémon journey.
There's a fanfic where Ash catches Mew and Mewtwo during a special tournament. The story focuses on how Ash has to face off against powerful trainers who also have their eyes on Mew and Mewtwo. It's a great read as it shows Ash's growth as a trainer and how he strategizes to keep these two Pokémon safe from those who might misuse their power.
There are 'Ash Catches Mew' fanfictions where Ash catches Mew accidentally. He might be trying to save Mew from some other danger, like a group of poachers. In the heat of the moment, Mew decides to trust Ash and goes into his Pokéball. This unexpected turn of events then leads to a whole new adventure as Ash has to deal with the implications of having caught such a rare and powerful Pokémon.
Well, in a fanfiction about Ash catching Mew, there could be a plot where a time - traveling device gets involved. Ash accidentally travels back in time to a period when Mew was more common. He has to adapt to the different environment and rules of that time. There, he meets a young Professor Oak who is also on a quest to find Mew. Together, they embark on an adventure. Along the way, Ash shows his determination and love for Pokemon, which makes Mew interested in him. Eventually, Ash manages to catch Mew, but he also has to figure out how to get back to his own time with his new, very special Pokemon.
In some versions of the 'ash catches mew fanfic', Ash might have a special encounter with a legendary Pokémon trainer who gives him a rare item or some advice on how to catch Mew. This encounter could be the turning point in his quest. And sometimes, Mew itself may be in a situation where it's more vulnerable, which gives Ash the opportunity to attempt the catch.
Pikachu would most likely be there. Since Pikachu is Ash's closest companion, it would be involved in any story related to Ash. Maybe Pikachu could also have some sort of interaction with Mew, like being a bit jealous at first of Ash's new connection with Mew.
His Pikachu might feel a bit jealous at first. But eventually, they would all accept Mew as part of the team. Ash would have to spend more time getting to know Mew's unique abilities, which might mean less training time for the others temporarily. However, in the long run, Mew could teach the other Pokemon some new tricks.
In fanfiction, the relationship between Ash and Female Mew can be very interesting. It often involves unique storylines where Ash might encounter Mew in a different context than in the original Pokémon series. For example, the fanfiction could explore how Ash's adventures change when he has a special bond with Female Mew. Maybe they go on a journey together to discover new Pokémon or face a powerful enemy that only they can defeat as a team. This relationship in fanfiction can bring out different aspects of Ash's character, such as his compassion and determination in a new light.