Yes, there are likely some fanfics out there with this concept. The 'Harry Potter' universe and the idea of the Infinity Stones from the Marvel universe are both very popular, so some creative fans might combine them in their fan - created stories.
One way they could interact is through a magical accident. Maybe a wizard accidentally casts a spell near an Infinity Stone and it creates a rift between the two universes. Characters like Harry Potter could then be drawn into the Marvel universe. They might be initially confused by the high - tech and different power systems in the Marvel world. For example, the Infinity Stones' power to control reality, time, etc. would be a new concept to Harry who is used to magic like spells and potions.
One way could be through a powerful dark wizard's experiment. Maybe a wizard, seeking ultimate power, discovers a way to bring the Infinity Stones into the magical world. They could be hidden as powerful magical artifacts, and their powers might be harnessed in a way similar to how wizards use magic. For example, the Time Stone could be used to manipulate time within the wizarding world, perhaps to reverse a tragic event or to gain an advantage in a battle.
One possible fanfic could be about a wizard from the Harry Potter world accidentally stumbling into the Marvel universe. The wizard discovers the Infinity Stones and realizes their immense power. He teams up with the Avengers to protect the Stones from a dark wizard who wants to use them to conquer both universes. The story could involve the wizard using his magic in unique ways to help the Avengers in battles and the Avengers teaching the wizard about their world.
He might become extremely powerful. The Infinity Stones have the power to manipulate reality, time, space and more. Harry could use it to defeat Voldemort in a much easier way. For example, with the Time Stone, he could go back in time to prevent certain events that led to Voldemort's rise or stop him from ever being born.
Let's say Hermione found an Infinity Stone. She would immediately start researching it. She would scour the Hogwarts library and use all her knowledge of magic. She might try to find a way to control it or at least contain its power. She could also consider the ethical implications of such a powerful object. Would it be like a Horcrux? Should it be destroyed? These are the kinds of questions she would ask herself.
One key element is the power of the Mind Stone itself. It can be about how characters interact with its mind - controlling abilities. For example, a hero might struggle against the Stone's influence.
It could bring back powerful wizards. For example, if a wizard like Merlin was resurrected using the power of the Infinity Stones, it would change the power balance in the wizarding world. He could have knowledge and magic far beyond what is currently known, and his return could either help in the fight against evil or cause new problems if his views are different from the modern wizards.
You can start by looking on popular fanfic websites like Archive of Our Own (AO3) or FanFiction.net. Just use the search bar and type in relevant keywords like 'Harry Potter' and 'Infinity Stone' to see if any such fanfics pop up.
In a fanfic, the Infinity Stones could be the key to unifying the two universes. For example, the Soul Stone could have a connection to the souls of wizards in the Harry Potter world. A villain from the Marvel universe could try to use the Stones to gain control over the magic in the Harry Potter world. The Avengers and the main characters from Harry Potter would then have to work together. They would combine their skills, with the Avengers' combat abilities and the wizards' magic, to stop the villain from achieving his evil plan. The fanfic could explore how the different powers and cultures of the two universes interact and co - exist during this adventure.