You can try Archive of Our Own (AO3). It has a vast collection of fanfictions, and you can easily search for 'Arthur Saves Merlin' within the Merlin fandom section. There are likely to be many different takes on this theme there.
One common theme is loyalty. Arthur's loyalty to Merlin is what drives him to save Merlin in most of these fics. It shows that their relationship is not just about master - servant but also about true friendship.
In some fanfictions, Arthur saves Merlin from a magical creature that has been sent specifically to target Merlin because of his powerful magic. For example, a dark wizard sends a shadow demon after Merlin, and Arthur, with his courage and swordsmanship, manages to slay the demon and save Merlin. This often leads to a deeper bond between them as they realize how much they mean to each other.
One popular 'Merlin Saves Arthur' fanfiction might be 'The Saving Grace' where Merlin uses his magic in a really creative way to rescue Arthur from a powerful dark sorcerer. It's full of action and shows the deep bond between them.
These fanfictions often explore different scenarios that weren't shown in the original series. It gives fans a chance to see new adventures and how Merlin would handle difficult situations to save Arthur. For example, in some fanfics, Merlin has to make difficult choices between using his magic openly or secretly to save Arthur, which adds an extra layer of intrigue.
One great 'arthur saves merlin fanfic' could be 'The Rescue by the Lake'. In this fic, Arthur discovers Merlin in a perilous situation near the enchanted lake. He bravely battles the dark magic that has Merlin trapped and manages to free him. It's a really exciting read.
The banter between Merlin and Arthur in fanfiction is really interesting. It can range from light - hearted jabs at each other's habits. Merlin might poke fun at Arthur's love for jousting and how he always gets a bit too competitive. Arthur could retort by mentioning Merlin's clumsy attempts at serving him. Their banter also reflects the underlying respect they have for each other despite their different social standings. It's like a friendly sparring that keeps their relationship dynamic.
The 'Redemption' trope is also seen in some fanfictions. Maybe Arthur has made some mistakes in the past, and Merlin helps him to redeem himself. Or vice versa. It's a way to explore the characters' growth and development. And then there's the 'Battle Against Evil' trope where they fight side by side against dark forces, which really showcases their bond and loyalty.
I really like 'The Sword in the Stone' as a fanfiction - like take on Merlin and Arthur. It shows Merlin as this wise and mysterious figure guiding Arthur on his journey to become king. There are also some great interactions between the two characters that show the deep bond they share. You can find it in many libraries or online bookstores.
Merlin would likely be seen as a bit of an enigma at Hogwarts. His magic is different from the norm, so he might be a bit of an outsider at first. But his kind heart and loyalty would soon win over his classmates. Arthur would be the brave and headstrong character, perhaps a bit like a Gryffindor version of his usual self. He'd be eager to learn about combat magic and would probably be a natural leader in group projects or Quidditch teams.