Maybe it's an ancient and powerful dragon that has been in hiding for a long time. This dragon decides to raise Natsu for some prophecy - related reasons. It could be that the dragon believes Natsu is the key to saving the dragon or human world from a great danger.
One possible plotline could be Natsu developing unique magical abilities different from his canon ones due to being raised by another dragon. Maybe he has a different way of controlling fire or even some new elemental powers.
It could be a water - based dragon. In that case, Natsu might have some water - related magic in addition to his fire magic. This would make him a very unique character as he would be able to combine two opposing elements in a way that no one else in the Fairy Tail guild could.
One possible plot could be that Natsu, while being raised by the female dragon, learns unique dragon magic that is different from what he would have learned otherwise. He might develop a special bond with the dragon, like a mother - son relationship, and the story could follow his adventures as he uses the skills taught by the dragon to protect the dragon's lair or the surrounding area from threats.
One possible plot could be that Natsu is raised by a dragon other than Igneel. This new dragon might have different values and teachings. For example, if it was a more reclusive dragon, Natsu might be less outgoing and more reserved compared to his canon self. The dragon could also teach Natsu different types of magic, which would change the way he fights and interacts with others in the Fairy Tail guild.
He might be more in tune with nature. Since dragons are often associated with nature, Natsu could have a deeper respect and understanding of the natural world around him, showing more kindness to animals and plants.
Maybe it's another dragon, a malevolent one, who sees the female dragon's act of raising a human as an abomination. He decides to target Natsu to prove a point or to gain power over the female dragon. The malevolent dragon could try to undermine Natsu at every turn, creating numerous challenges for him.
One idea could be that Natsu discovers unique magical abilities passed down from the Dragon God that set him apart from other mages. For example, he might be able to communicate with all types of dragons, not just the ones he's related to in the original story.
In a fanfic where Natsu is raised by a light - dragon, his character would develop in a very different way. The light - dragon's influence would likely make him more of a beacon of hope. He would be more focused on justice and helping others in a more positive, guiding light - kind of way. His powers would be different, and he would have to learn to control light - based abilities. This would require a different kind of self - discipline compared to controlling fire. His relationships would also be affected. For instance, he might be more of a role model to the younger members of the guild, and his interactions with his enemies would be more about converting them to the side of good rather than just defeating them.
One possible plot could be that Natsu is raised by a water - dragon instead of Igneel. This would give him different elemental powers and a different personality. He might be more calm and collected, having the influence of the water - dragon's nature. He could also have a different relationship with his guildmates, as his powers would interact differently with theirs.