It's possible in fanfiction, but it would be a huge departure from the established canon. In terms of how it would change the story, the entire plot of the series would need to be re - imagined. For example, Percy's initial discovery of his parentage would be much more complex. Instead of the straightforward revelation of being Poseidon's son, there would be the added mystery and confusion of Hera's involvement. His place at Camp Half - Blood might also be questioned more, as Hera has a different standing among the gods compared to Poseidon.
Percy's relationship with the other campers at Camp Half - Blood would be a rollercoaster. The children of Poseidon might feel a bit betrayed or confused, as they thought Percy was one of their own. However, Percy could use his new status to bridge gaps between different cabins. For example, he could work with the children of Aphrodite to improve relationships in the camp, since Hera has some connection to love and relationships in a different way than Aphrodite. With the gods, his relationship with Zeus would be extremely strained, given Zeus's past issues with Hera. But he might find new allies among the gods who are friendly with Hera, like Hephaestus. Overall, Percy's relationships would be a mix of challenges and new opportunities.
Percy's powers would be more complex. He could have the ability to communicate with sea deities in a different way. Maybe he could use Hera's diplomatic skills to make deals with them or resolve disputes. His control over water could also be extended to other substances that have a connection to water, like steam or ice, in a more efficient way than before. And his powers of persuasion, which could be influenced by Hera, might be used to calm angry sea storms or make sea monsters cooperate with him, which is an interesting combination of his Poseidon - given powers and Hera - influenced skills.
If Percy were the son of Poseidon and Hera, his powers would be quite unique. His water powers could be enhanced in a different way. Maybe instead of just controlling water, he could transform water into different substances related to Hera's domain, like turning water into a fertile soil - like substance for plants to grow. His leadership skills would be off the charts. He could use his Poseidon - given strength and Hera - influenced charisma to lead not just demigods, but also other mythical creatures. He might also have the power to protect a place or a group of people in a more profound way, like creating a shield made of both water and a golden energy that represents Hera's protection.
His powers might become more related to Hera's domain. For example, he could gain some control over marriage and family bonds. He might be able to sense when relationships are in trouble or strengthen the loyalty between people. Also, his existing powers could be enhanced in a way that reflects Hera's influence. Maybe his water - based powers could be more refined and have a new aspect to them, like being able to purify water to heal emotional wounds as well as physical ones, since Hera is associated with purity in some ways.
A plot idea might be that Percy is magically transported to a time when Poseidon and Hera had a major disagreement in the past. He has to use his wits and powers as Poseidon's son to prevent this rift from growing and causing chaos in the present. Also, he could be given a task by Hera to rescue one of her favored heroes who has been trapped by a sea monster under Poseidon's domain. This would put Percy in a tricky situation where he has to balance his loyalty to his father and the task given by Hera. He might also encounter a group of demigods who are descendants of both Poseidon and Hera in some way, and together they have to face a common enemy.
When it comes to his relationship with Hera herself, it would be complex. At first, Percy might be resentful or confused about being adopted by her. But as time goes on, he might start to understand her in a way no one else does. Hera could start to see Percy as a true son, and this could lead to a deep, if somewhat unusual, bond between them. Percy would have to balance this new relationship with his existing ones, and it could lead to some really interesting character development and story arcs.
In addition to his water - based powers, Percy as the son of Hera and Poseidon could have enhanced leadership abilities. Hera is often associated with ruling and leadership. So, he might be able to inspire and lead groups more effectively. He could also have a stronger connection to the sky, as Hera has some associations with the heavens. This could give him the ability to control weather elements related to the sky, in addition to his control over water.
His relationship with Annabeth would likely be more complex. She might be initially worried about the new powers Percy has from Gaia. There could be some jealousy or fear that he's becoming too different. With his friends from Camp Half - Blood, some might look up to him more because of his even greater potential, while others could be intimidated. His relationship with the Poseidon cabin would also be different. They might see him as more of an enigma now that he has this additional connection to Gaia.
Well, in the original Percy Jackson lore, Percy is the son of Poseidon and Sally Jackson. But in a fanfic where he's the son of Artemis and Poseidon, it would be a wild departure. Artemis is a virgin goddess, so this goes against the traditional mythology. However, in fanfic, anything is possible. Maybe the story could start with some kind of magical interference that results in this unexpected parentage. The plot could then explore how Percy deals with being the son of two such powerful and different deities. He might struggle with the expectations of both Artemis' domain of the hunt and the sea - related powers of Poseidon.
In this fanfiction scenario, Poseidon's relationship with Percy would be full of twists and turns. At first, Poseidon might be shocked and a bit angry. How could his son be related to Leto? But as time goes on, he realizes that Percy is still his son and that this new connection could be used to their advantage. He starts to work with Percy more closely, guiding him on how to balance his powers from both Poseidon and Leto. They might have some father - son talks about the new responsibilities Percy has and how he can use his dual heritage to protect the world better. Poseidon could also start to see Percy as more of an equal, as he is now part of a more complex and powerful family tree.