They might interact with a sense of mutual respect at first. Jon, knowing Myrcella's position as a princess, shows her due courtesy, while Myrcella is intrigued by Jon's different upbringing and his skills. They could exchange stories about their lives, like Jon telling Myrcella about the Wall and the wildlings, and Myrcella sharing tales of the Red Keep.
A fanfiction could revolve around Myrcella being a key figure in helping Jon Snow claim his rightful place in the Seven Kingdoms. Since she has been exposed to the politics of King's Landing, she could use her knowledge and influence to support Jon, who has his own claim through his Targaryen heritage. Their story could be about uniting different factions and bringing a new era of peace to Westeros.
In some fanfiction, Jon Snow and Myrcella could form an alliance to bring peace between the North and the South. Myrcella, being a princess, has the influence in the South, and Jon has the loyalty of the North. They work together to end the feuds and power struggles, and along the way, they develop a deep friendship that might turn into something more romantic.
Perhaps Myrcella is sent to the Wall as part of a political maneuver. There she meets Jon Snow. At first, they are at odds, but as they get to know each other, they find common ground. They learn of a conspiracy that threatens both the North and the South of Westeros. Together, they embark on a journey to expose the conspiracy and save the kingdoms. This would involve them facing many obstacles, including distrust from their own people and powerful enemies who want to keep the conspiracy hidden.
You can try fanfiction websites like Archive of Our Own (AO3). It has a vast collection of fanfictions from various fandoms, and there's a good chance you'll find some related to Jon and Myrcella there.
There could be a fanfiction where Jon discovers Myrcella's hidden strength. In this story, they start as acquaintances and gradually develop a deep bond. Their story might be filled with adventures and moments of self - discovery as they support each other through various difficulties.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.