Another power Percy could get is the ability to teleport through water. In the fanfiction, the trident could be a key to opening portals within water bodies. This would give Percy a huge advantage in battles and in his adventures, as he could quickly move from one place to another across the world's oceans.
He could gain the power of enhanced water control. The trident being a symbol of the sea god's power, Percy might be able to manipulate water on a much larger scale, like creating huge tidal waves or even controlling the water inside living beings.
One possible power is the ability to see through illusions more easily. Since the Kyuubi is a powerful entity, a doujutsu from it could give Naruto an edge against genjutsu users. It could break through complex illusions that would otherwise trap him.
He could gain the power of super strength that far surpasses his demigod strength. This would allow him to lift extremely heavy objects or even mountains. Another power might be the ability to control the very essence of the ocean on a global scale, not just local waters like he could as a demigod.
Maybe he could gain the ability to transform into an Egyptian animal, like a falcon or a jackal. This would be a cool addition to his existing powers and would give him new ways to move around and fight enemies.
He could gain the power of controlling water like Poseidon's kids since he has good chakra control. It would be a new addition to his skill set.
He might become an even more powerful figure. The trident could enhance his abilities to control water and perhaps give him new powers related to the sea. He could use it to defend his friends and fight against stronger enemies.
In Percy Jackson fanfiction, a trident tattoo could symbolize a connection to Poseidon. It might mark a character as a demigod related to Poseidon or as someone with a special mission or allegiance to the sea god. Maybe it's a sign of power, as the trident is Poseidon's main weapon.
One possibility is that Percy uses the trident to explore uncharted areas of the ocean. He discovers ancient underwater ruins that are protected by powerful magic. With the trident, he can navigate through dangerous barriers and uncover secrets about his own heritage and the history of the sea gods.
The trident might represent Percy's growth. It could mean that he has reached a new level in his development as a demigod, and Poseidon is acknowledging that with this gift. It's like a rite of passage in a way.
In some fanfictions, Percy might obtain the trident through a special quest. Maybe he has to prove himself worthy to an ancient sea deity who then bestows the trident upon him as a symbol of power and trust.
He might gain enhanced physical strength. The devil gene could give him a boost in his taijutsu skills, allowing him to overpower opponents more easily.