I'm not entirely sure specifically as there could be many different takes on it. Generally, it might be about Naruto having some sort of connection to a character named Yami. Maybe Yami is a new character introduced in this fanfiction who has a special relationship with Naruto, perhaps as a father figure or some other significant bond.
Well, Naruto is a given as the main character in 'Naruto son of Yami fanfiction'. Yami is another key character. We might also see characters like Jiraiya. Since he was Naruto's mentor in the original series, he could play an important role in helping Naruto understand his connection to Yami. Hinata could also be an important character, perhaps her feelings for Naruto are affected by this new revelation. And then there could be antagonists from Yami's past or present who oppose Naruto because of his relation to Yami.
Yami remains alive in the manga. The author chose to keep Yami as an ongoing character to drive the story forward and interact with other characters in various scenarios.
As far as I know, Yami doesn't die in the manga. The story might have twists and turns, but that particular event hasn't happened yet. Maybe there are rumors or speculations, but based on the official storyline, no.
One plot idea could be Yami going on a solo mission to a mysterious and dangerous land. He has to face powerful new enemies and discover secrets about his own past. Another could be Yami training a young and inexperienced magic knight, sharing his unique combat and magic knowledge.
To write a believable characterisation of Yami, focus on his rough exterior but also his loyalty to his squad. Show his love for food, especially Japanese food. Also, don't forget his unique magic style and how he uses it in combat.
A possessive Yami can create a sense of mystery in the fanfiction. Readers might wonder why he is so possessive. Is it love? Loyalty? Or something else? This can keep them engaged and eager to find out more about his motives.