One common theme could be loyalty. Merlin is often extremely loyal to Arthur, and when he breaks a rule, Arthur's punishment might be a test of that loyalty. Another theme could be power dynamics. Since Arthur is the king and Merlin has magic which is often a secret, the punishment could be related to maintaining the balance of power in Camelot.
Common themes in such fanfiction include justice. Arthur, as the king, has to uphold justice in Camelot. So if Merlin does something that goes against the laws or Arthur's expectations, he has to be punished. Another theme is friendship. The punishment might strain or strengthen their friendship. It could also be about secrecy. Since Merlin's magic is a secret, Arthur's punishment could be related to Merlin keeping that secret better, like restricting his movements to ensure he doesn't accidentally expose his magic.
In 'Arthur punishes Merlin fanfiction', a frequent theme is growth. Arthur might punish Merlin in a way that forces Merlin to grow as a person or in his magical abilities. For example, if Merlin misuses his magic, Arthur could make him train harder with it. Also, the theme of forgiveness often plays a part. After the punishment, there is usually a moment of understanding and forgiveness between the two characters.
One common theme is friendship. Their relationship is often at the heart of the stories, showing how they support and grow with each other. Another is loyalty. Arthur and Merlin are extremely loyal to each other in the original series, and this is often emphasized in fanfiction.
I'm not sure of specific 'Arthur punishes Merlin fanfiction' offhand. You could try searching on fanfiction websites like Archive of Our Own. They have a large collection of fanfics related to the Arthur and Merlin fandom.
One common theme is the exploration of gender roles. Since it's a male pregnancy, it challenges the traditional ideas of male and female roles. Another theme is the deepening of the relationship between Merlin and Arthur. The pregnancy often serves as a catalyst for them to become closer and more reliant on each other.
One common theme is loyalty. Since they are brothers, their loyalty to each other is often a central focus. They will go to great lengths to protect one another.
Love, in different forms, is a recurring theme. It could be platonic love that is so strong it's like a family bond. Or it could be a romantic love that the authors explore in a very subtle or sometimes more obvious way. This love is often what drives them to make sacrifices for each other in the fanfiction stories.
One common theme is the power dynamic. Since Merlin has magic and Arthur is the king, it's interesting to see how a female Merlin would handle that. Another theme is love and loyalty. Their relationship, whether it's platonic or romantic, is often at the center.
In Merlin and Arthur gay fanfiction, a prevalent theme is the exploration of identity. Arthur, as a prince, has certain expectations placed on him, and exploring his identity as a gay man is a significant aspect. Merlin, too, with his magical abilities and his role as a servant, has his own identity journey. Another common theme is the idea of sacrifice. They might be willing to sacrifice their own desires or positions for the sake of the other, which is a very romantic and noble concept often explored in these fanfictions.
Another theme is the test of their relationship. The hotel can be a place full of challenges and temptations. It could be other people trying to come between them or some difficult situations that make them question their loyalty to each other. Like in some fanfictions, a powerful sorceress at the hotel tries to charm Arthur away from Merlin, but they overcome it and their relationship becomes stronger.
One common theme is loyalty. In these fanfictions, Merlin's loyalty to Arthur takes on a new, more intense dimension when there are romantic feelings involved. Another theme is sacrifice. Often, either Merlin or Arthur is willing to sacrifice a great deal for the other, which is a big part of their relationship in these stories.
Love and protection are common themes. Arthur's possessiveness often comes from his love for Merlin and his desire to protect him from harm. For example, in many fanfics, Arthur will not allow others to harm or even insult Merlin.