Well, his sacrifice would likely have a huge impact. For Zoe, she might be filled with guilt and a new sense of purpose. The other characters like Annabeth could be deeply affected too. Annabeth might be angry at first that Percy made such a choice, but then she could use that anger to fuel her own actions in the story. His sacrifice could also inspire the other demigods to be braver and more selfless in their own quests.
It could be that Percy's sense of honor led him to sacrifice himself for Zoe. If he had made a promise to protect her, he would uphold it no matter what. Also, Zoe might have been the key to solving a major mystery or threat. Percy, realizing this, chose to sacrifice himself so that Zoe could continue and complete whatever task was necessary. Additionally, his love for his friends and the greater community of demigods might have made him believe that Zoe's survival was more important than his own.
The other characters would likely be filled with grief. His friends would probably feel a deep sense of guilt, wondering if there was something they could have done to stop him. Artemis herself might feel a heavy burden, knowing that Percy sacrificed his life for her. She may vow to honor his memory in some way.
I'm sorry I can't directly recommend a specific 'Percy sacrifices himself for Artemis' fanfic. But you can try searching on fanfic platforms like Archive of Our Own (AO3). There are tons of fanfics there, and by using relevant keywords in the search bar, you might be able to find one that suits your interest.
Perhaps it's when Percy actually makes the sacrifice. He stands there, facing whatever danger it is, and as he gives himself up, there's a moment of complete silence. His body might start to glow or something, signifying his life force being given away, and his friends can only watch in horror.
Percy could be a brave and adventurous character, perhaps with some special abilities like being able to control water or having enhanced strength. Zoe might be a smart and resourceful female character, maybe with skills in tracking or archery. They could be from a fictional world full of magic and mythical creatures.
In fanfiction, Naruto sacrificing himself for Obito could be a very emotional and dramatic concept. It might show Naruto's ultimate selflessness, believing that Obito is worth saving at the cost of his own life. This could be due to Naruto seeing the good in Obito that others might not, like the part of Obito that was once a kind - hearted shinobi.
When Batman sacrifices himself in fanfiction, it can also be a way to explore the darker side of Gotham. Maybe his sacrifice was in vain, and the city falls deeper into crime and corruption. Or perhaps it leads to a new kind of hero emerging, inspired by Batman's last act. It could also show how the villains react, some might be glad that their nemesis is gone, while others may feel a strange sense of loss as Batman was always a worthy opponent.
One scenario could be that they are facing a powerful monster. The monster is about to strike Annabeth, and Percy jumps in front of her at the last moment, taking the fatal blow. Another possibility is that they are in a dangerous situation like a collapsing building or a sinking ship, and Percy uses his powers to ensure Annabeth's escape while he stays behind and perishes.
Perhaps in the fanfic, there is a prophecy that states only a hero's ultimate sacrifice can save Artemis from a dark curse. Percy, being the selfless hero he is, decides it has to be him. He goes through a series of trials first, trying to find an alternative way but in the end, he has no choice. He sacrifices his life force to break the curse on Artemis. This act not only frees Artemis but also has far - reaching consequences in the Percy Jackson universe, like changing the power dynamics between the gods and demigods.