If the OC is a powerful sorcerer or sorceress, they could use magic to either control Joffrey's actions or to protect the innocent from his wrath. For example, they could cast spells to make Joffrey see the consequences of his actions in his dreams, which might make him change his ways or at least make him more cautious.
An OC who is a master strategist could form alliances with other powerful houses in Westeros. They could then use these alliances to put pressure on Joffrey's regime. They might also use their strategic skills to outwit Joffrey in battles of wits, such as during courtly intrigue and political negotiations, gradually weakening his hold on the Iron Throne.
One idea could be an OC who is a healer in King's Landing during Joffrey's reign. The OC secretly tries to undermine Joffrey's cruel rule by using their medical knowledge to help those he persecutes. They might start by treating the families of those unjustly imprisoned. This could lead to a dangerous game of cat and mouse with Joffrey and his cronies as they suspect someone is working against them.
Joffrey is often characterized as even more cruel and unhinged in fanfiction. His violent outbursts and lack of mercy are sometimes exaggerated. Margaery is usually shown as a very intelligent and manipulative woman. She uses her beauty and charm to her advantage.
The OC can be developed by showing their initial fear and confusion when they first hatch the dragon. For example, they might not know what to do with this powerful and dangerous creature at first. As time goes on, they learn to bond with the dragon, which in turn builds their confidence and sense of purpose.
Joffrey was a cruel character. It's hard to imagine a traditional love story for him. His nature was so malicious that any form of love seemed out of place. He was more interested in power and causing pain. So, in the context of the show, a real love story for him seems almost impossible.
The OC could have a unique power that directly counteracts Superman's. For example, if Superman has his heat vision, the OC could have the ability to absorb and redirect energy. This would make their encounters very intense and give the OC an edge in battles.
One possible fanfiction could be about Joffrey's brother Tommen growing into a wise and just ruler. He could be shown learning from the mistakes of his older brother. He might start secretly training in combat and political strategy, with the help of some of the more noble characters in the series, like Tyrion perhaps. He could then start to make changes in King's Landing, trying to reverse the chaos that Joffrey had caused.
Start with understanding Joffrey's character deeply. Read and re - read his parts in the books or watch his scenes in the show. Capture his essence, both his cruel side and any possible redeeming qualities. Then, create a unique plot. Maybe your self - inserted character has some secret knowledge from the modern world that can change Joffrey's fate. For example, knowledge of medicine to prevent some of the plagues in Westeros.
There could be a really interesting fanfic where a Dragonborn enters the world of Game of Thrones during Joffrey's reign. Maybe the Dragonborn would initially be seen as a threat by Joffrey. But the Dragonborn's powers could change the power dynamics in King's Landing. For example, if the Dragonborn has the ability to control dragons, it would be a huge advantage over the Lannisters who rely mainly on their wealth and military might at that time.
In the context of the fanfic, the Dragonborn's presence could also expose Joffrey's weaknesses more clearly. The people of Westeros, seeing someone with such great power (the Dragonborn) who is not as cruel as Joffrey, might be more inspired to rise up against Joffrey. And Joffrey's own allies might start to question their loyalty to him when they see the Dragonborn as a potential new power player in the game of thrones.
It was Olenna Tyrell and Petyr Baelish. They conspired to have Joffrey poisoned at his own wedding.