Maybe he could gain the power of prophecy. In the Naruto world, he has a strong connection to destiny. In the Percy Jackson universe, this could translate to the power of seeing the future related to the quests and battles against the Titans or other threats. Also, his connection to the Nine - Tails could give him some sort of fire - based power that is enhanced by the magic of the Percy Jackson world, making it more effective against the mythical beasts there.
In this fanfiction, Naruto might gain the power of flight. In the Percy Jackson universe, there are various ways characters can fly, like on the back of a pegasus or using winged shoes. Given Naruto's adaptability, he could somehow develop this ability. His existing ninja skills could also be enhanced by the magic of the Percy Jackson world. For example, his transformation jutsu could be made more powerful, allowing him to transform into more than just people or animals, but perhaps into mythical creatures from Greek mythology. This would give him an edge in both stealth and combat situations within the new universe.
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.
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 might gain enhanced physical strength. The devil gene could give him a boost in his taijutsu skills, allowing him to overpower opponents more easily.
Well, Naruto reincarnated as a Fox God could potentially gain the power of illusion - casting on a grand scale. Since foxes are often associated with trickery in myths, he could create illusions that are almost impossible to break. His connection to the spiritual world might also be strengthened, allowing him to communicate with other spirits or even draw power from them. And of course, his physical strength would be enhanced to match his new divine status.
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.
He might gain a more powerful form of Rasengan, like a Rasengan that can change its shape and properties according to the situation. Maybe he has better control over his Nine - Tails chakra and can use it in more creative ways without losing control.
Another possible power is the ability to control all the elements with extreme proficiency, not just the ones he already has in the original series. He could combine them in ways never seen before, creating powerful and unique jutsus that could defeat any opponent.
In a 'Percy Jackson, Naruto, The Forgotten God' fanfiction, perhaps the forgotten god has some power that is crucial for both their worlds. Percy Jackson might come from his world where Greek gods exist and Naruto from his ninja - filled land. They are brought together by some prophecy. They start their journey, facing enemies from both their universes who don't want the forgotten god to be found. Along the way, they learn from each other's fighting styles and ways of life.
There could also be a situation where Naruto is like a father figure to the younger demigods. He could comfort them when they are homesick or feeling down. He would share stories from his own life in the ninja world, which could inspire the demigods to be brave and persevere in the dangerous world of Percy Jackson.
Well, it could be that Naruto, with his ninja skills, enters the world of Percy Jackson. Maybe he teams up with Percy to fight some common enemies like the Titans or other mythological creatures. Naruto's jutsus would be a cool addition to the battles in the Percy Jackson universe.
He could probably gain the ability to phase through objects. Just like wraiths are often depicted as being able to pass through solid things. This would give him an edge in combat and also in sneaking around.