If Jon meets Rhaegar, it could change the story drastically. For one, Jon might gain a new understanding of his Targaryen heritage. He could learn secrets about his family that were lost over time. This new knowledge could influence his decisions regarding the Iron Throne and his relationships with other characters.
One possible plot could be that Jon, after learning his true identity, travels back in time and meets Rhaegar. Rhaegar could see the potential in Jon and start training him in the ways of leadership and combat. This would be a great way to explore their relationship and how Rhaegar's influence might shape Jon's future decisions.
Well, in many fanfictions, after Jon meets Daenerys, they might face challenges from external enemies or internal politics. Maybe they have to unite different factions to survive. Or, their relationship could face tests due to their different backgrounds and goals.
There are. Many fanfictions on this topic play with the idea of time travel or different storylines within the 'Game of Thrones' universe. For example, in some, Lyanna is able to see Jon's journey and influence his decisions in a way that was not possible in the original story. They can be really interesting reads if you're into exploring different character interactions.
Perhaps Jon Snow and Drogon meet in a desolate place. Jon is alone and injured, and Drogon, instead of attacking, shows a strange compassion. Jon, using his wits, figures out how to communicate with Drogon. They then form an unlikely bond, and Drogon helps Jon get back to civilization. This would be a great character - development - based fanfiction scenario.
One possible plot could be that Jon Snow, on his journey north of the Wall, somehow gets lost or is magically transported to where Daenerys is. They immediately recognize each other's importance. Jon, being the honorable man he is, offers his help to Daenerys in her quest for the Iron Throne. Daenerys, in turn, is intrigued by Jon's tales of the North and the White Walkers. They form an alliance early on, which changes the course of the entire Game of Thrones story, with their combined forces being a formidable power in Westeros.
Well, the theme of redemption often plays a part. Lyanna may see her actions in a new light through meeting Jon, and Jon may find a sense of purpose through this new connection with his mother. Also, the exploration of the Stark heritage is common. How Lyanna's influence can shape Jon's understanding of his Stark side more deeply.
In addition to Jon and Daenerys, other characters might also play important roles in some fanfictions. For instance, Tyrion Lannister could be there as an advisor to Daenerys. His wit and political acumen might help in the interactions between Jon and Daenerys. Or Arya Stark could be involved in some way, perhaps as a spy or a messenger between the North and Daenerys' camp. These additional characters can add more depth and complexity to the story of Jon and Daenerys' meeting.
In the fanfiction world, Jon Snow meets Drogon and there could be an instant connection. Since Jon is a Targaryen (in the show's revelation), Drogon might sense a kinship. They could form an alliance. Jon could use Drogon to gain an upper hand in battles or to travel quickly across Westeros. It would be an amazing sight to see Jon Snow on the back of Drogon, flying over the kingdoms.
In fanfiction, when Jon Snow meets Daenerys in Essos, they might immediately form an alliance. Jon could be impressed by Daenerys' dragons and her strength. They may start to discuss their common goals, like fighting the White Walkers. Their meeting could also spark a romantic interest between them, as they are both strong - willed leaders.