Character development is a key element. Writers often focus on how Aryia's vengeful side and her Stark upbringing interact with Tywin's Lannister pride and his political ambitions. For example, in some fanfics, Aryia's skills as a fighter might be pitted against Tywin's strategic mind in a tense showdown.
One popular Aryia and Tywin fanfic is 'The Unlikely Bond'. It explores an interesting relationship between the two characters, with Aryia's feisty nature clashing and then gradually forming an unexpected connection with Tywin's calculating demeanor.
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.
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.
There is a fanfic titled 'Arya and Tywin: A Different Path'. In this story, the author takes a unique approach to their relationship, showing how Arya's skills and Tywin's power might interact in unexpected ways. It's really a fascinating read. There are also some works that focus on how Arya might outwit Tywin in his own game of politics.
You can start by looking on fanfiction websites like Archive of Our Own. There are a large number of 'Tywin Lannister fanfic' there. Another place could be some dedicated Game of Thrones fan forums where fans often share their own works.
At first, their interaction would likely be very guarded. Sansa would be cautious as she has learned to be in a world full of danger. Tywin would probably see her as a young, naive girl but also a valuable asset. As time goes on, Sansa might start to challenge Tywin's ideas, which could lead to some intense exchanges between them.
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.
First, study the characters of Arya and Tywin thoroughly. Know their personalities, motives, and backstories. Then, come up with an interesting premise for their interaction, like a secret alliance or a battle of wits.
You can try some popular fanfic websites like Archive of Our Own (AO3). There are often a lot of well - written Arya and Tywin fanfics there. Just search for the relevant tags and you might discover some great stories.