This is something I have a few ideas and tips about it. But I also have a cautionary warning about it too. First:

Characters reading and/or viewing stories is a way to make them somewhat relatable. After all, it is what you are doing now. But be careful on what they read. It adds to their characteristics about their interests. A wrongful and inappropriate story for the character can ruin the story about them. Having them read similar stories of their interests or broaden their knowledge on a particular subject is a safe way to do it.

Second. If they are not reading a story of their interests, give them a reason to be reading it. For example, character A is reading something of a shelf owned by character B. Character A is curious about what the book he picked is about. After checking it character A felt disgusted. Character B is interested in stories that character A felt is cringy.

This example plays into the dynamic of characters A and B.

Third, and it is the path that I've taken. Using it as a way to explain how a character from one of your story to know about another character from an another story. Let me explain.

I have two separate stories. One is what I called the Death series, and the other is what I called the multiverse series. A character from the multiverse series reads about from my Death series. She was at odds about it at first. Then she kept reading about it and enjoyed the plot.

I did this as a way to have a certain character to have knowledge about the other. A story reading about an another story by the same author. In a way it is clever. Two things a writer could play with when doing this.

1. A merging of two stories. Or at least a crossing of one stories character into another. But the plot is the most important when one is attempting to do so. A poor plot means a bad crossover.

2. Separate but knowledgeable. Well at least one would know about another or vice versa.

Even a possibility of both. This was done in by a writer called One whom made One punch man and Mob Psycho 100 where both main characters read up on the other's tale.

What story your character read is up to you. But always, always give credit to authors whose works you included into your own. Not doing this is a violation of Wattpad terms and usage. Unless the author whose story you burrowed or incorporated from gave you a written permission. DO NOT ACCEPT ANY VERBAL AGREEMENTS.