I'm not sure specifically as there could be many different interpretations in fanfiction. It might be about Ash, from the Pokémon series, having an encounter with Dialga and perhaps trying to catch it in a unique or unorthodox way compared to the regular Pokémon - catching scenarios in the official series.
A popular Pokemon Dialga fanfiction is 'Dialga's Time - Twisted Adventure'. It takes Dialga on a journey through different timelines, which is really exciting. You get to see how Dialga interacts with different versions of the Pokemon world and other Pokemon. The story is full of twists and turns as Dialga tries to fix the disruptions in time that it encounters along the way.
One idea could be a story where the balance between the different dimensions overseen by Dialga (time), Palkia (space), and Giratina (the distorted world) is disrupted. Arceus, as the creator deity, has to step in. Maybe a powerful, unknown force is causing chaos, making time and space fold in on each other. Giratina, usually banished to the Distortion World, finds itself drawn back into the normal world, causing all sorts of mayhem. Dialga and Palkia try to fix things on their own but realize they need Arceus' help. The fanfic could focus on their journey to restore order and the sacrifices they might have to make along the way.
Obviously, Ash, the young and enthusiastic Pokemon trainer, is one of the main characters. He is always eager to take on new challenges and catch new Pokemon. And then there's Dialga, a majestic and mysterious Legendary Pokemon. In this fanfiction, their interactions and adventures together are likely to be the focus. Ash's human qualities and Dialga's otherworldly powers will probably create a lot of interesting situations.
Another theme is redemption. Giratina is an exiled Pokemon, and in many fanfics, its relationship with Dialga can be a path towards redemption. For example, Dialga may offer a way for Giratina to atone for its past actions through their connection.
The allure of Pokemon Dialga fanfiction lies in its ability to expand on the already rich lore of Dialga. Dialga is such a powerful and mysterious legendary Pokemon. Fanfiction allows us to explore its powers in more depth, like its control over time. It also gives us a chance to see Dialga in different scenarios, whether it's in battles we haven't seen in the official games or anime, or in relationships with other Pokemon.
A plot twist could be that the powers of Dialga, Palkia, and Giratina are actually interchangeable. In a moment of extreme crisis, they merge their powers and identities, creating a new, super - powerful entity. This entity has the combined abilities of controlling time, space, and the distortion world. However, this also comes with a cost as they lose their individual identities. Arceus then has to decide whether to allow this new entity to exist or try to separate them back into their original forms.
You can try looking on fanfiction websites like FanFiction.net or Archive of Our Own. They have a large collection of Pokémon - related fanfictions and there's a good chance you'll find the 'Ash Catches Dialga' one there.
One possible plotline could be Ash and Dialga going on an adventure together through different time - periods, facing challenges unique to each era. Another could be Dialga using its time - related powers to help Ash in his Pokemon battles in unexpected ways.
There's a fanfic titled 'Dialga and Giratina: A Reconciliation'. In this, it starts with their long - standing differences. But as the story progresses, through various events and challenges they face together, they begin to understand each other more. It's really interesting to see how the author develops their characters.