There is a fanfic named 'Baby Yugi and His Friends' that focuses on the relationships Yugi had as a child. It gives a lot of cute and heartwarming moments between Yugi and his closest pals. This fanfic really delves into the innocence of that time in Yugi's life. For example, it shows how they used to play games together and how Yugi's unique personality was starting to show even at a young age.
Another one is 'The Origins of Yugi Muto' which is a fanfic that not only looks at baby Yugi but also starts to set the stage for how he would become the person he is in the main series. It gives some backstory to his family and how his environment influenced him. It's a great read if you want to understand more about the roots of Yugi's character.