One possible plot for such a fanfiction is that the squirrel mask has been stolen by an enemy. Minato's spirit appears to Naruto and tells him about the importance of the mask. Tsunade, as the Hokage, organizes a mission to retrieve it. Naruto, with his determination and the help of his friends, embarks on this mission. Along the way, he discovers new abilities within himself that are somehow related to the mask and his father Minato's legacy.
The plot could be that the squirrel mask is a key to an ancient power. Minato knew about it but passed away before he could fully explore it. Naruto stumbles upon the mask and Tsunade warns him of the potential dangers. However, Naruto's curiosity gets the better of him. He starts to have visions of Minato, who gives him clues on how to unlock the mask's power. Eventually, Naruto uses this power to protect the village from a new threat.
Their relationships could be explored through flashbacks. For instance, we could see how Minato interacted with Tsunade when he was alive. Maybe he sought her advice on certain matters, or they had some joint missions. This would give us insights into their respect for each other.
It's possible that in the huge world of fanfiction, someone has written a story about Minato getting Tsunade pregnant. However, the Naruto fanfiction community is so diverse that it could be buried among thousands of other stories. Also, the Naruto canon doesn't really suggest such a relationship, so it would be a very creative and perhaps controversial take in fanfiction.
A plot could revolve around Minato's spirit guiding Naruto and Tsunade in a difficult situation. For example, there's a mysterious illness spreading in the village and Minato's spirit gives them clues on how to find a cure. Or perhaps a story where Naruto, Minato, and Tsunade are all trapped in a genjutsu - created alternate reality, and they have to find a way to break free while also learning some important lessons about themselves and their relationships.
The story would be wild. Naruto would have a different family dynamic. With Tsunade as his mother, he might have more access to medical ninjutsu knowledge from a young age. Minato's speed and intelligence combined with Tsunade's gambling habit could make Naruto a more unpredictable character. Also, the way the village views him could be different. Since Tsunade is from the Senju clan, Naruto would have a stronger connection to the village's founding family, which could lead to different political situations within Konoha.
Naruto would receive very diverse training. From Minato, he would learn about space - time ninjutsu. Minato was known for his Flying Thunder God Technique, and Naruto could inherit the knowledge to develop his own version. As for Tsunade, she would train him in close - combat skills. Naruto would learn how to throw powerful punches and use his chakra in a more brute - force way. Also, he'd learn about the importance of chakra control in medical ninjutsu from her.
In the 'naruto has a mask fanfiction', it might be that Naruto finds the mask himself. He could stumble upon it during one of his adventures, perhaps in an ancient ruin or a hidden cave. The mask could be enchanted or have some special property that draws Naruto to it, and he decides to keep it and figure out its secrets on his own.
In fanfiction, Naruto and Minato often represent a connection between generations. Minato was a great ninja in his time, and Naruto is following in his footsteps. Fanfictions can explore how Naruto lives up to his father's reputation.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide variety of themes and scenarios, some of which might be rather strange or controversial. However, Naruto fanfiction often explores different relationships and alternate storylines, but this particular one seems a bit unorthodox and I haven't personally come across it.