It's hard to give an exact time as it depends on the manga's plot development. But typically, Yuta Okkotsu shows up when certain events and character arcs lead to his introduction.
Maki in fanfiction usually has a fierce loyalty to her friends, especially Yuta. She is the type to fight for what she believes in. Yuta is sometimes portrayed as being a bit naive in the ways of the world outside his own small circle, but his pure heart makes him endearing. In many stories, their different personalities create an interesting dynamic, like in a story where Maki's boldness gets them into a risky situation and Yuta's calm thinking gets them out.