Mythology means stories that are sometimes made up or not true but people believe in them because they are special to them. Vatican City is a very special place because it's where the Pope lives and where the important leader of the Catholic Church is. The mythology of Vatican City is all about the stories of the people who believe in God and Jesus and all the other holy people.
One of the most important stories is about a man named St. Peter. The story goes that he was the very first Pope and he was chosen by Jesus himself. He was a very important person and people believe that he's still watching over Vatican City even though he passed away a long, long time ago. That's why there's a big church called St. Peter's Basilica in the center of Vatican City.
Another important story is about the Holy Spirit. People believe that it's a special part of God and that it helps people understand and follow the teachings of the Catholic Church. There's a special day called Pentecost where people celebrate the Holy Spirit coming down to earth and giving people the ability to speak in different languages so they could communicate with each other.
There are also many stories about the different saints who are considered holy and special by the Catholic Church. One example is St. Francis of Assisi who is known for his kindness to animals and his love for nature. People believe that he's watching over Vatican City too and that he can help them if they ask for his help.
So basically, the mythology of Vatican City is all about the special stories and beliefs of the people who follow the Catholic Church. It's important to them because it helps them feel closer to God and to the holy people who have come before them.