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.
A great plot could be that the dragon egg was placed in Jon Snow's path deliberately by someone with a grand plan. As Jon Snow delves deeper into the origin of the egg, he uncovers a conspiracy that dates back to the time before the events of the main 'Game of Thrones' story. Along the way, he forms an unlikely alliance with a group of characters, all while protecting the dragon egg from those who would use it for destruction.
Jon Snow could interact with the dragon egg through his dreams. In the fanfic, the egg might communicate with him on a spiritual level while he sleeps. These dreams could give him clues about the egg's power and what he is supposed to do with it. Also, he may touch the egg and feel a jolt of energy, which makes him realize that there is something truly special about it.
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 some fanfictions, the dragon egg might be the key to uniting the North and Daenerys. Jon Snow, being a Targaryen in some theories, has a special connection with the egg. It could hatch a dragon that recognizes Jon as its true master and helps him in his battles for the Iron Throne and the protection of the realm. This would be a major turning point in the power dynamics of Westeros.
The dragon egg can also lead to Jon Snow exploring his Targaryen heritage more deeply. Since dragons are closely associated with the Targaryens, he starts to learn about the history and magic of his family. This new knowledge changes his perspective on his place in the world. He might start to embrace a more Targaryen - like leadership style, which is different from his Stark - influenced upbringing. For example, he could become more flamboyant and bold in his strategies, rather than the more cautious Stark way. And all of this development is intertwined with the mystery and potential of the dragon egg.
One popular 'Jon Snow Black Dragon' fanfic is 'The Bond of Ice and Dragon'. It tells a story where Jon Snow forms an unexpected connection with a black dragon. The story is filled with adventure and a touch of magic.
One common theme is power. The dragon gives Jon Snow a great deal of power, and these fics often explore how he wields it. Another theme is identity. Since Jon Snow has a complex identity, and the addition of a dragon connection further complicates it. There's also the theme of destiny. Fics may show that Jon Snow was always meant to have a connection with a dragon as part of his greater destiny in Westeros.
A great 'Jon Snow a dragon' fanfic is 'Jon Snow and the Dragon's Destiny'. In this fanfic, Jon is mysteriously drawn to a hidden dragon lair. There, he meets a young dragon that has been waiting for him. Together, they set out on a journey to uncover the secrets of Jon's past and how it is intertwined with the dragon's existence.