Yes, there are some out there. You can start by looking on fanfic websites like Archive of Our Own. Just search for 'Joffrey Baratheon gay' and you'll likely find a variety of stories. However, the quality can vary greatly, so be prepared to sift through some to find the ones that are well - written.
One common theme is the redemption of Joffrey. OC characters are often used to try and reform his cruel nature. Another theme is power struggle. The OC may get involved in the power dynamics in Joffrey's court. And love or romance can also be a theme, where the OC might develop a romantic relationship with Joffrey or be involved in his love life in some way.
Some fanfictions might focus on an alternate universe where Joffrey is not a king. He could be a simple knight, and the story could explore how his personality would develop without the power and privilege of the throne. He might learn humility and honor in a different way.
One can expect a lot of creativity. Since Joffrey is such a complex and often - hated character in the original series, in gay fanfics, authors might try to redeem him or show a different side of him. There could be new storylines involving his relationships with other male characters, perhaps with a focus on his growth or downfall in the context of these relationships.
One great Joffrey Baratheon OC fanfiction is 'The Redemption of Joffrey'. It presents an original character who tries to reform Joffrey. Another is 'Joffrey's Unlikely Ally' which shows how an OC gets involved in Joffrey's court politics in a very interesting way. And 'A Different Joffrey' which gives a new perspective on his character through the eyes of an OC.
Yes, there could be fanfiction that focuses on their complex relationship in a non - sexual or inappropriate way. For example, it might explore their power dynamics within the family, their political ambitions, and how they interact with other characters in the Game of Thrones universe. Such fanfiction can provide interesting insights into their characters without delving into improper content.
In some fanfictions, Joffrey is re - imagined as a more sympathetic character. His cruel actions are often explained as a result of his upbringing and the political pressures around him.
Another aspect is their individual insecurities. Joffrey's need for validation as a king and Cersei's fear of losing her power and influence. A well - written fanfiction could delve into how these insecurities play out in their relationship and how they try to overcome or use them to their advantage.