One plot idea could be Arya, in disguise, getting close to Tywin as a servant in King's Landing. She could overhear his plans and use that knowledge to try and undermine the Lannisters from within. Another could be a scenario where Tywin discovers Arya's true identity but decides to keep her alive for some strategic reason, perhaps to use her as a bargaining chip against the Starks. And a third idea might be a story set in an alternate universe where Arya and Tywin form an unlikely alliance against a common, greater threat, like a White Walker invasion in the south before the events at the Wall.
Maybe in the fan fiction, Tywin discovers Arya's true identity but decides not to kill her immediately. Instead, he tries to use her as a pawn against the Starks. He might try to train her in the Lannister ways, which would put Arya in a difficult position of having to resist while also trying to find a way to outwit Tywin.
Arya and Tywin could also interact in a more unexpected way. Maybe in a situation where they are forced to work together for a short time due to some external threat. During this time, Arya has to constantly remind herself of her ultimate goal of revenge while Tywin is constantly on guard against her, yet also seeing potential in her skills for his own purposes.
Their relationship could develop in a very complex way. At first, Arya would be full of rage towards Tywin. However, if she were to be captured by the Lannisters and Tywin were to show her a different side of himself, perhaps a more paternal side (even if it's just a ploy), Arya might start to question her hatred. On the other hand, Tywin might see Arya as a potential asset, someone he could mold in his own image. This could lead to a relationship that is part mentor - mentee and part captor - captive, with a lot of power dynamics and emotional turmoil.
Well, in fan fiction, Arya might not be as afraid of Tywin as she potentially was in the original series. Since fan fiction allows for more creative freedom, she could have some special powers or skills that give her an edge over Tywin. Their interaction could then be more of an equal battle of wits and wills, rather than the one - sided power dynamic that was somewhat implied in the original.
One great Arya and Tywin fanfiction is 'The Unlikely Encounter'. It beautifully portrays the first meeting between them and how Arya's quick thinking saves her from Tywin's wrath. Another good one is 'Alliance of Convenience' which explores the idea of them working together against a common enemy. It's full of political intrigue and character development.
In Arya and Tywin fanfiction, their dynamic can be really interesting. Tywin is a shrewd and powerful figure, while Arya is a fierce and determined young girl. One aspect could be a scenario where Arya, in her quest for vengeance, crosses paths with Tywin. Maybe she tries to infiltrate his court or army in disguise. Their interactions would be filled with tension as Tywin would likely see her as a threat, yet be intrigued by her boldness. It could lead to a complex power struggle within the story.
There are several good ones. 'Tywin's Ascent' is a fanfic that details his rise to power. It gives a lot of background on his family and the challenges he overcame. 'The Mind of Tywin' is really interesting as it tries to get into his thought process. It shows how he made decisions that shaped the Westeros we know. And 'Tywin's Last Stand' is a fanfic that imagines his final days in a very creative way.
Power is a very common theme. Since Tywin is all about power in the original story, fanfictions often explore how he gains, maintains, or loses power in different scenarios. Family dynamics is another one. His relationship with his children, especially Tyrion, Jaime, and Cersei, is always a rich area for exploration in fanfictions.
One common theme is the clash of their different worlds. Arya is a young, vengeful girl from the North, while Tywin is a powerful, calculating lord from the Westerlands. Their interactions often explore this contrast.