One possible plot could be the son growing up in the shadow of his mother's power-hungry ways. He might struggle with the expectations placed on him due to his family name. For example, he could be groomed to be a political pawn but secretly desires a more peaceful life away from the power struggles of King's Landing.
He could influence events by being a voice of reason in Cersei's court. If he's intelligent and perceptive, he might be able to persuade his mother to make more diplomatic decisions rather than always resorting to force.
In an interesting fanfiction plot, Cersei's son could be exiled from King's Landing. During his exile, he forms a band of outcasts. Together, they build a new community away from the power struggles of the capital. As he grows, he realizes that his mother's way of ruling is wrong. Eventually, he returns to King's Landing with his new - found wisdom and tries to overthrow his mother's tyrannical rule, not to take over but to establish a more democratic and fair system for the people of Westeros.
An OC who is a skilled assassin would be a good choice. They are hired to kill someone in King's Landing but cross paths with Cersei. Cersei, instead of having the OC killed, decides to use their skills for her own purposes. The assassin has their own code and ethics, which would constantly be at odds with Cersei's methods.
Sansa Stark could be an interesting pairing. It could be a story of two strong - willed women from opposing sides. They could either become bitter enemies or, in a more creative take, find common ground and form an unexpected alliance. Also, Margaery Tyrell is a great character to pair with Cersei. Their power struggle in the show was fascinating, and fanfiction could take it in new directions, like Margaery actually befriending Cersei and showing her a different way to rule.
One idea could be that the OC is a healer from a far - off land who comes to King's Landing. Cersei initially distrusts the OC but as time passes, she realizes the OC's skills are invaluable, especially when it comes to treating her children's ailments. This could lead to a complex relationship where Cersei struggles between her pride and her need for the OC.
Perhaps Cersei's son, having grown up seeing the chaos his mother caused, could bring about a new form of governance. Instead of the feudal system that was prevalent, he could introduce a more democratic - like system where the voices of the lords and the common folk are heard. This would be a huge change from the power - hungry struggles that were characteristic of the Game of Thrones world.
Perhaps in the fanfiction, Cersei's son discovers a hidden power within himself. He uses this power not for domination like his mother would, but to heal the broken kingdom. He might travel across the land, learning from the common people and using his new - found abilities to bring prosperity.
Yes, there are quite a few out there. Some focus on how Cersei's pregnancy would change her power dynamics in King's Landing. For example, in some fanfictions, her pregnancy makes her more vulnerable to political attacks as her enemies see an opportunity to undermine her while she is in a physically weaker state due to pregnancy. However, the quality of these fanfictions can vary greatly.
There's also 'Jaime and Cersei: The Unwritten Chapters'. This fanfiction fills in the gaps between the events shown in the show. It gives more in - depth exploration of their emotional states, especially during the times when they were separated, and how they coped with the challenges to their relationship.