If Percy is thrown back in time, his powers could be enhanced. In the past, magic and the power of the gods were more prevalent. The very air might be charged with more divine energy. His ability to communicate with sea creatures could expand, as there could be species that are now extinct or have evolved in his own time. However, he might also face limitations. For example, if he goes back to a time when the gods were at war, some of his powers related to Poseidon might be restricted depending on his father's situation in that war.
His powers would likely be both strengthened and challenged. Strengthened because in the past, the gods' influence was more immediate and powerful. The water itself could hold more 'life' in it, so his hydrokinetic abilities could be more potent. But at the same time, he would be in an unfamiliar environment. There could be ancient magic or curses that could interfere with his powers. He might have to learn new ways to use his powers in harmony with the different magical rules of the past time period. For example, in some ancient times, using powers in a certain way might be considered taboo and could draw unwanted attention from powerful beings.
His water - based powers might be affected in different ways. If he goes back to a time when the oceans were less polluted, the purity of the water could make his powers stronger. However, if he goes to a time when the gods were more in control of the elements, they might be able to limit his power. For example, Poseidon might have more say over how Percy can use water powers if they are in the same time period.
His powers might not be affected at all. Percy's connection to water is more about his essence as a demigod rather than his physical form. So he could still control water, summon sea creatures, and heal himself with water just as well as before.
His water - controlling power would be a huge advantage. For example, during naval operations, he could manipulate the sea to create safe passages or disrupt enemy ships. Simple as that.
The balance in nature would be disrupted. Artemis is the goddess of the hunt, the moon, and nature. Her death could cause strange phenomena in the natural world, like animals going wild or the moon's cycle becoming erratic. This would not only affect the demigods but also mortals who depend on the stability of nature.
His relationship with his father Poseidon would be different. He might see a side of Poseidon that he never knew before, like when Poseidon was younger and less experienced. This could change how Percy views his father and their connection.
One idea could be Percy going back in time to the era of the first Olympian gods and having to deal with the raw, unbridled power of those early deities. He might find himself in the middle of a power struggle between Zeus and his father, Kronos, before the Titanomachy. Another plot could involve Percy trying to prevent a major disaster in the past that has far - reaching consequences in his own time. For example, stopping the release of a powerful monster that was supposed to be sealed away long ago.
His powers could be more nature - based. For example, instead of just controlling water, he might be able to control all forms of liquid in nature, like sap or blood. His connection to the wild could also make him more attuned to the emotions of animals, allowing him to communicate with them more effectively.
Well, in a fanfiction where Percy is born in Greece, his powers would likely have a more 'Greek - flavoured' aspect. Since he's in the homeland of the Greek gods, his connection to water could be intertwined with the Greek concept of the four elements. So, his water powers might interact more with the other elements in a way that is more in line with Greek elemental theory. He might also be able to draw on the power of Greek water deities more directly, which could enhance his abilities and give him new ways to use his powers in battles and other situations.
Well, instead of summoning water or having a connection with the sea, he might have the power to shift shapes, a common ability associated with Loki. He could turn into different animals or even other people to gain an advantage in a fight or to infiltrate an enemy's stronghold. Also, his power over fire could be enhanced, as Loki has some association with fire in Norse mythology. He could use this to create distractions or attack opponents from a distance.
His powers would likely become more god - like. He might gain the ability to control lightning, like Zeus. Also, his strength and speed could be enhanced to a much greater degree. His control over water, which was his main power before, could also be amplified and perhaps combined with his new lightning powers in some unique ways.