It might be a story where Harry delves into the family magic in order to solve some sort of mystery. For example, he could be looking for a way to defeat a new dark force and realizes that the family magic holds the key. He could learn new forms of magic related to protection or divination that are unique to his family.
Obviously, Harry Potter himself is a very important character as the story revolves around him learning family magic. His friends like Hermione and Ron might also be important as they could support or help him in his journey of learning this magic.
It could be an older relative who was thought to be dead but actually has been living in seclusion, waiting for the right time to teach Harry about their family magic. This relative might have a vast knowledge of the family's magical traditions and spells.
In some fanfictions, Harry might learn family magic that has to do with time manipulation. His family could have had a special talent for seeing into the past or future. As he delves into this magic, he has to learn to control it carefully, as misusing time - related magic can have serious consequences. He may use this new - found magic to prevent certain disasters or to gain knowledge from the past that could change the course of the wizarding world.
In this type of fanfiction, a great plotline could be that Harry stumbles upon a hidden family grimoire. Inside, he finds magic that was thought to be lost. For example, there could be spells for creating protective shields that are stronger than any known spell. Or perhaps he discovers family magic that is related to time - travel, which he then has to learn to control carefully so as not to disrupt the timeline. This discovery of family magic would add a whole new layer to his character development and his role in the wizarding world.
One main theme is self - discovery. Harry realizing his ability for wandless magic is like finding a new part of himself. Another theme is breaking boundaries. Since wandless magic is not as common in the wizarding world shown in the original books, it represents going beyond the normal magical practices. And of course, there's the theme of growth, as Harry has to learn and develop this new skill, which often comes with challenges and setbacks.
Well, it could be that Harry has an encounter with an Egyptian wizard who decides to teach him their unique brand of magic. This magic might involve things like controlling the sands or communicating with mummies. Through his learning, he gains new powers and uses them to face his enemies in a different way than before.
One interesting plotline could be Harry discovering a new and ancient form of magic that was lost for centuries. This could lead him on a journey to understand its origin and how to master it.