Some fanfictions give Harry the power of elemental control. He can manipulate fire, water, air, and earth. This power often comes in handy during duels as he can create barriers of fire or gusts of wind to deflect spells. It also makes him a more formidable opponent against dark wizards who don't expect such a wide range of powers from him.
One special power often seen in Harry Potter fanfiction is the power of resurrection. A character might have the ability to bring the dead back to life, which would have a huge impact on the wizarding world. It could change the course of battles and relationships. Another power could be the power of premonition on a much more detailed level. Instead of just having a few hazy visions like in the books, a character could see the exact future events, including what spells will be cast and who will be where at a given time. Also, some fanfictions feature characters with the power to manipulate magic itself, being able to change the rules of how spells work or even create entirely new spells that no one has ever seen before.
Some fanfictions give Hermione the power of time - travel. This power is not like the time - turner she used in the original books which had limitations. In these fanfictions, she can freely travel through time, go back to correct mistakes, or gain knowledge from different eras which she can then use to improve the present situation at Hogwarts or in the wizarding world.
One interesting storyline could be that Harry discovers his moon powers during a full moon at Hogwarts. Maybe he can communicate with magical creatures that are only active during the full moon. Another could be that his moon powers are linked to a hidden prophecy, and Voldemort wants to steal those powers for himself.
One cool power often seen in such fanfiction is teleportation. This allows characters to quickly move from one place to another, escaping danger or arriving at crucial moments just in time. There are also powers related to healing, where a character has an extraordinary ability to cure any injury or illness, which can be very useful in the often - dangerous wizarding world.
Well, there are often powers like mind - over - matter. In these fanfictions, a character might be able to manipulate objects just by thinking about it. So, instead of using the Wingardium Leviosa charm, they could simply make an object fly towards them or change its shape just with their thoughts. Also, there could be a power of elemental control. A character could have the ability to control fire, water, earth, and air to a great extent, like creating massive storms or making volcanoes erupt at will.
Well, there are fanfictions where Harry has godlike powers such as the ability to resurrect the dead. This completely changes the dynamic of the wizarding world as it goes against the natural laws of magic in the original series. Another aspect could be his mind - having the power to read and control the thoughts of every living being, making him almost omniscient and omnipotent within that fictional world.
In some fanfictions, Harry Potter's healing factor might be linked to his connection with ancient magic. For instance, when he is injured in a battle, the dormant ancient magic in his veins awakens and heals his wounds almost instantaneously. This could also have the side effect of enhancing his overall magical abilities as he recovers. It might be seen as a sort of magical evolution within the context of the fan - created story.
In some fanfictions, Harry Potter might have a phoenix as a magical familiar. The phoenix could help him in dangerous situations with its healing tears and ability to teleport. Another example could be a magical cat, like a Kneazle. A Kneazle is intelligent and could warn Harry of approaching danger or help him find hidden things.
One super power often seen in such fanfiction is elemental manipulation. A character could have the power to control all four elements - fire, water, earth, and air - with great precision. They might be able to create huge firestorms to fend off dark wizards or summon tsunamis within the Hogwarts lake. There are also super strength powers where a wizard or witch can lift extremely heavy objects, like the entire Hogwarts castle, which comes in handy during battles against powerful dark forces. And of course, there's the power of invisibility without the need for an invisibility cloak, which gives a character an edge in spying or sneaking around.
In some 'Harry Potter' fanfiction, an interesting anime - like power could be the ability to control elements in a way similar to characters in 'Avatar: The Last Airbender' which is often incorporated. For example, a character might be able to manipulate water with great precision, not just for simple spells but for complex formations like creating ice sculptures mid - battle. Another could be a power of super speed, allowing them to move through Hogwarts corridors so fast that they seem to disappear, much like the Flash in DC Comics but with a more magical, 'Harry Potter' - ish twist.