Jon Snow could discover that the dragon has some sort of special connection to his true heritage. Maybe it was left there by his Targaryen ancestors. The dragon could help him uncover secrets about his family and his place in the world. He may also face challenges in controlling the dragon at first, but with time, he masters it and uses it to change the fate of Westeros.
Well, in this fanfiction, it's possible that the dragon egg has some special connection to Jon Snow's true parentage. It could be a sign of his Targaryen heritage, if we follow the theories. He could then use the dragon that hatches from the egg to fight against the White Walkers, as dragons are very powerful creatures in the 'Game of Thrones' universe.
In this fanfiction, it could be that the dragon is actually a key to unlocking some ancient magic or prophecy. Jon Snow, finding the dragon beyond the Wall, realizes its significance. He teams up with the dragon, and together they embark on a journey to find out more about this magic. Along the way, they face many challenges, both from the natural elements beyond the Wall and from the political intrigue brewing in the Seven Kingdoms as word of the dragon spreads.
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.
One common theme is adventure. Jon's discovery of the dragon eggs often leads him on a series of exciting adventures as he tries to protect or hatch the eggs. Another theme is power. Dragon eggs symbolize great power, so stories often explore how Jon deals with the implications of having such power at his disposal.
An author who has a passion for exploring alternate storylines in the 'Game of Thrones' world could be the one to write an amazing 'Jon Snow finds a dragon' fanfiction. This person might be someone who was disappointed with the original show's ending regarding Jon Snow and wants to give him a more epic and dragon - filled adventure. They could draw on different elements from the books and the show to create a unique and engaging story.
In the fanfic, Jon might use the dragon egg to gain power. He could try to hatch it and form an alliance with the dragon. This would change the power dynamics in Westeros completely. Maybe he'd face opposition from other powerful houses who fear his newfound strength.
Perhaps in the fanfic, Jon is a dragon trainer in disguise. He finds a dragon that has been lost from its group. He uses his skills to communicate with the dragon and tries to reunite it with its kind. Along the way, they face many challenges and obstacles together.
In a 'Jon Snow and Daenerys meet' fanfiction, they might initially be suspicious of each other. Jon, being the honorable man he is, could be cautious about Daenerys' claim to the throne. Daenerys, on the other hand, might see Jon as a potential threat or an ally she can use. They could start by exchanging stories of their respective journeys, with Jon talking about the Night King and the threat from the North, and Daenerys sharing her experiences in Essos. Eventually, they might form an alliance to fight their common enemies, and who knows, perhaps there could be a romantic connection between them as well.
Jon Snow could use the castle as a base to improve relations with the other kingdoms. He might hold diplomatic meetings there, inviting lords and ladies from all over Westeros. This would be a big change from his more battle - focused past.
In some fanfictions, Jon Snow could gain control over a dragon. Given his special connection to the supernatural, it's not entirely far - fetched. This would make him an extremely powerful player in the Dance of Dragons, able to tip the balance of power in any direction he chooses.