Perhaps there is a crossover event in the fanfiction. Some sort of magic or powerful artifact causes the Naruto universe and the world of Poseidon to collide. Naruto, being the adventurous and powerful character he is, gets involved in this chaos and ends up having a special relationship with Poseidon, either as an ally or having to face him as an adversary.
One plotline could be that Naruto is chosen by Poseidon to be his champion in the human world. He is given special powers to protect the seas and their secrets from those who would misuse them. Naruto, with his determination, uses these new powers to fight off evil forces that are threatening the ocean's balance.
It could be a rogue sea god who is jealous of Poseidon's power and wants to use Naruto to get to him. This sea god might try to manipulate Naruto into believing that Poseidon is a threat to his village and convince him to attack Poseidon first.
Well, it could be about Naruto having special powers related to Poseidon. Maybe he can control water in ways that are different from his normal ninja skills. He might also have a connection to the sea or underwater realms.
Maybe Poseidon decides to test Naruto by sending various sea monsters after him. Naruto, with his determination and the help of some new underwater friends he makes, has to fight these monsters and prove himself worthy. This could lead to a deep friendship between Naruto and Poseidon in the end.
You can try websites like Archive of Our Own (AO3). It has a large collection of fanfictions across various fandoms, including those related to Poseidon. Just use the search function and type in 'Poseidon' to find relevant stories.
Naruto might initially struggle with the power of the Trident. Since he's used to his chakra system, the magic or divine power of the Trident would be something new. He could start by accidentally activating some of its basic powers, like creating small whirlpools or summoning small sea creatures. As he spends more time with it, he would learn to control it better, maybe even combining his own ninja techniques with the Trident's power, like using the Rasengan while channeling the Trident's energy through it.
One character could be Jiraiya. He could have known something about Naruto's true heritage all along and be the one to finally reveal it to Naruto. From the Greek side, Triton, Poseidon's son in mythology, could be a character. He could either be a rival or an ally to Naruto. In the ninja world, Shikamaru might be involved. His intelligence could be used to help Naruto understand and strategize with his new powers, especially when dealing with any threats that come his way because of his connection to Poseidon.
Well, if Naruto had Poseidon's trident, it would completely change the power dynamics in the Naruto universe. Firstly, the trident is a symbol of great power in Greek mythology. Naruto could use it to control water in ways that are unimaginable in the Naruto world. He might be able to create massive tidal waves to defend Konoha or use water to enhance his already existing jutsus. Also, it could potentially give him an edge in battles against powerful foes like Madara or Kaguya. With the trident, Naruto could become an even greater protector of his village and the entire ninja world.
Well, it could be that Poseidon's Trident has been stolen and Naruto is called upon to find it. He teams up with some of Poseidon's loyal servants or maybe even a mermaid or two. Along the way, he uses his ninja skills to track down the thieves. When he finally finds the Trident, he has to face the main villain who stole it. Naruto might use his Rasengan in combination with the power of the Trident to defeat the bad guy and return the Trident to Poseidon.