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.
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.
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.
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.
One possible plot could be that there is some sort of magical or unforeseen event that causes this situation. Maybe a strange jutsu goes wrong and creates an unexpected bond between them. Then they would have to deal with the consequences, both personally and within the context of the Hidden Leaf Village.
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.
She might be initially shocked. Given her own past traumas and her relationship with Naruto, she could be hesitant at first. But then, considering Naruto's lonely situation, she might warm up to the idea and show a more maternal side towards him.
Well, if Tsunade were Naruto's mother in fanfiction, it would likely change the story a great deal. For one, Naruto might have had a more stable upbringing in the village. Tsunade could have protected him from some of the early hardships he faced, like being ostracized for having the Nine - Tails. Also, Naruto might have learned medical ninjutsu much earlier from Tsunade, which could have added a new dimension to his fighting style. And perhaps he would have had a more confident personality from the start, since Tsunade is a strong - willed and confident character herself.
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.