Yes, there are. You can find some on fanfiction platforms like Archive of Our Own. Some might explore their complex relationship within the Hogwarts setting, perhaps delving into how their different personalities interact.
You could also try some Harry Potter - focused fanfiction communities on social media platforms like Reddit. Some users might share their own Snape x Quirrell fanfiction or recommend good ones that they've read.
Perhaps Harry is tricked. Quirrell could be using some sort of mind - influencing magic or deception. He might make Harry believe that giving him the stone is the only way to save his friends or Hogwarts. Harry, being young and inexperienced, might fall for such a ruse and hand over the stone without fully realizing the consequences.
One possible consequence could be that Voldemort, who is using Quirrell, gains more power. Since the Philosopher's Stone has the ability to create the Elixir of Life, Voldemort could use it to create a new body or regain his full strength much faster. This would put Hogwarts and the entire wizarding world in great danger as Voldemort is extremely powerful and evil. He would likely start to hunt down those who oppose him, especially Harry Potter, with even more vigor.
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A really unique part of these fanfics is how they can change our perception of Quirrell. Instead of just seeing him as a simple villain, they can show his inner turmoil. Some fanfics might depict him as a victim of certain circumstances or having a more complex moral compass. Also, the relationships he forms in fanfics can be different from what we expect. He might have unexpected friendships or alliances that add new layers to the story.
In some fanfictions, they might rewrite the possession scene completely. Instead of the typical way it was shown in the books, they could add new magical elements. Maybe Quirrell has some hidden magic that reacts to the possession, creating a more complex and engaging story.
One great 'Harry Potter Quirrell fanfic' is 'The True Nature of Quirrell'. It delves deep into his character, exploring his motives beyond what we see in the original books. Another one could be 'Quirrell's Hidden Past' which uncovers secrets about his life before Hogwarts. There's also 'Quirrell's Redemption' that offers an interesting take on if he could have been redeemed.
A great one is 'Quirrell's Hidden Struggle'. In this fanfic, it really shows how Quirrell's personality changes as he gets possessed. You can see the transformation from a timid professor to a more menacing figure under Voldemort's influence. It's interesting to see how the author plays with his character development.