They often start with a 'what if' scenario. For example, what if Harry had an ability related to elemental magic like controlling fire? Then they build on it, thinking about how it would affect his relationships. If he could control fire, he might be more feared by some and respected by others. They also consider how it would change the plot. Maybe he could use this ability to fight Voldemort in a completely new way.
Often, they tie the rare abilities to Harry's character arc. Let's say Harry has the ability to heal any wound instantly. This could start as something he discovers by accident. But as he learns to control it, it becomes a part of his growth. He might start using it to help his friends more selflessly, which in turn makes him a more empathetic and powerful wizard. Writers use this to show his development and how his new ability shapes his identity within the fanfiction story.
In some fanfictions, Harry might have the ability to communicate with magical creatures on a deeper level than in the original books. For example, he could understand the thoughts and feelings of dragons, which gives him an edge in dealing with them.
His magical abilities would likely be developed in a more archaic and powerful way. The founders had different areas of expertise, so Harry could inherit a wide range of skills. Maybe he'd be a master of defensive magic like Salazar Slytherin was known for some aspects of it, and also be proficient in charms like Helga Hufflepuff was with her kind magic.
Rare abilities often act as a catalyst in the plot of Harry Potter fanfiction. Let's say a character has the ability to travel through time freely. This ability can disrupt the normal flow of events. They might accidentally change something in the past that has a huge impact on the present and future. It could lead to a situation where the main characters have to find a way to fix the timeline. Or if a character has the rare ability to control the minds of all magical creatures, they could use this power to either start a revolution among the creatures or to create an army, which would completely change the political and social structure of the wizarding world and thus drive the plot forward.
His magical abilities would likely develop at a much faster rate. The founders are extremely powerful and knowledgeable. They could guide Harry to discover and master magic that most wizards his age wouldn't even know exists.
They inherit his magical abilities through genetics in the wizarding world. Since Harry was a powerful wizard, his genes likely carry the magical potential which is passed on to his kids.
In Harry Potter fanfiction, a rare ability could be the power of true prophecy. While there are seers in the original series, in fanfic, a character might have the ability to see not just vague glimpses of the future but detailed and accurate prophecies that can change the course of the wizarding world. Also, the ability to heal any wound or illness instantaneously could be considered rare. This would make the character a sort of super - healer, far more powerful than Madam Pomfrey. And some fanfictions might explore the ability of a wizard or witch to transform into any object or creature at will, not just those within the Animagus transformation limits.
Well, in many Harry Potter fanfictions, characters develop new magical powers by making pacts or connections with magical entities. For example, a character could make a deal with a powerful magical spirit. In return for some service, the spirit grants them a new power. Also, some characters develop new powers through self - discovery and meditation. By delving deep into their own magical cores and understanding their true nature, they can unlock powers that were previously hidden. Additionally, training with a very powerful and experienced wizard can also lead to the development of new magical powers as they learn new techniques and ways of using magic.
His magical abilities might develop with a greater emphasis on intellectual magic. Since Rowena Ravenclaw is associated with knowledge and wisdom, Harry could be more inclined towards spells that require deep understanding and study. For example, he might master complex transfiguration spells earlier because Ravenclaw would encourage him to study the theory behind them thoroughly.
His magical abilities might be influenced by the Norse magic system. He could have a more primal and elemental approach to magic, perhaps being able to control natural forces like thunder (associated with Thor) or ice (linked to some Norse entities).
Harry could develop a more unique style of magic. His grandfather might have his own way of doing magic, and Harry would learn from that. For example, his grandfather could be more in tune with nature magic, and Harry would then incorporate that into his spell - casting, making his magic more diverse and less reliant on the traditional Hogwarts curriculum.