Another idea is that the discovery of Giovanni as his father makes Ash question his own identity and place in the Pokémon world. He might have to reevaluate his goals and his relationships with other characters. Meanwhile, Giovanni could be faced with the challenge of trying to make amends or trying to bring Ash into his world in a more positive way.
Often, it's portrayed as a complex relationship. Since Giovanni is typically seen as a villain in the Pokémon series, the fanfiction might show a struggle between Ash's good - natured self and Giovanni's more self - interested motives. For example, Giovanni might try to manipulate Ash into joining Team Rocket.
Sure. In the Pokémon community, there are numerous fan-created ideas. The idea of Giovanni being Ash's father has some interesting implications. It could potentially change the whole dynamic of Ash's journey. Fanfiction writers often take such unique concepts and run with them, so it's very possible to find such a fanfiction if you search in the right places, like some dedicated Pokémon fanfiction websites.
In this fanfiction, it could lead to a lot of interesting plot twists. For example, Ash might have a natural inclination towards Giovanni's style of leadership or strategic thinking without even realizing it. It could also create a great internal conflict for Ash as he discovers his true relation to a rather villainous figure in his world.
One possible plot could be Ash gradually discovering the truth. He might start noticing strange similarities between himself and Giovanni. Then, Giovanni could be torn between his role as the leader of Team Rocket and his newfound feelings for his son. Ash, on the other hand, would have to grapple with the idea of his father being a villain.
In some Pokemon fanfictions, there could be creative interpretations where Ash is made out to be Red's father. However, in the official Pokemon canon, there is no such relationship between them.
Ash might become more conflicted. He has always been on the side of good, but with Giovanni as his father, he'd have to grapple with his family ties. He could become more secretive and brooding as he tries to figure out how to balance his own values with this newfound family connection.
One common plot point is the revelation of their relationship. Usually, it's a big shock to Ash and the other characters. Another is Giovanni trying to protect Ash secretly while still being the leader of Team Rocket. Sometimes, there are also flashbacks showing how Giovanni might have been involved in Ash's early life in the fanfiction.
In fanfiction, evidence could be things like Giovanni having a soft spot for Ash that other characters don't notice. The author might write that Giovanni has some knowledge about Ash's past or abilities that seem to suggest a closer relationship. But this is just for the purpose of the fanfiction. In the canonical Pokemon world, Ash's father has not been officially revealed as Giovanni.
One plot idea could be that Ash's father was exiled from their town for a crime he didn't commit. The fanfiction could follow his journey to prove his innocence and his attempts to reunite with his family. Along the way, he could encounter unique Pokémon and make new friends who help him in his quest.