In fanfiction, Harry with a different wand can lead to all sorts of interesting scenarios. Maybe the wand has different magical properties that he has to learn to control. For example, it could be more powerful in certain types of magic but less so in others. This would force Harry to adapt his magical techniques.
Harry Potter's wand was made of holly wood, with phoenix tail feathers as the core. This wand, made by the famous wandmaker Garrick Ollivander, has a special connection to Voldemort's wand (made of ebony and dragon heartstrings), because they both come from the same phoenix tail feather. Harry's wand was about eleven inches long, and it was elastic, which made it very sensitive and accurate when it worked. This wand was very important to Harry, and it played a vital role in his fight against the Dark Arts.
While waiting for the TV series, he could also click on the link below to read the classic original work of "The Legend of Mortal Cultivation"!
Maybe an old, reclusive wand - maker who has been waiting for the right wizard to come along. This person could have a special intuition about wands and see something unique in Harry.
It could be a mysterious stranger. Maybe someone who has been observing Harry from afar and decides that he needs a different wand for some greater purpose. This stranger might have their own motives, perhaps related to a prophecy or a hidden plan within the wizarding world.
One reason could be Harry's pure heart. The Elder Wand might be attracted to his selfless nature. Another could be his connection to Voldemort. Since they are linked in many ways, the wand might see Harry as the key to resolving that conflict.
In many Harry Potter fanfics, the wand handle can be a significant detail. It might be made of unique materials like dragon bone or enchanted wood. Some fanfic authors use it to symbolize a character's personality or heritage. For example, a character with a dark past could have a wand handle made from a blackened, gnarled wood that gives off an ominous vibe.
One possible fanfiction could be about Harry using the wand to defeat the Basilisk in a more unique way than in the original story. Maybe he discovers a new spell with the help of the wand that can temporarily paralyze the Basilisk, allowing him to avoid its deadly stare more easily.
They could inherit it. Perhaps their family has a long - forgotten attic where the mithril wand has been stored for generations. One day, while exploring, they stumble upon it.
Well, it could be described in various ways. Maybe it has unique carvings on it, like ancient runes or symbols related to Harry's personal journey. It might be made of a special wood that's not common in the regular wand lore, like a wood from a magical tree only found in a hidden forest.
There's a chance that the maker is a new character, an old hermit wizard who lives deep in the Forbidden Forest. He has been observing Harry from afar and realizes that the wands available in the regular market are not sufficient for him. So, he uses his knowledge of forgotten magics to craft a custom wand just for Harry.