Well, there are fanfictions that explore Byleth's connection to the goddess Sothis in more depth. Maybe Byleth has to make a sacrifice to keep Sothis alive or has to deal with the consequences of Sothis' power going out of control. Also, some fanfictions might show Byleth training in a different style. Instead of the normal combat training in the game, they could be learning a secret art from an old master hidden in the mountains. And there are likely fanfictions that show Byleth's reactions to different endings of the game, like how they would handle the post - war situation in each of the possible routes.
Some great Byleth fanfictions might be those that put Byleth in a different time or place. Imagine Byleth in a modern - day high school setting but still with their unique abilities. It would be a really fun take on the character. Or there could be a fanfic where Byleth is sent to a different continent in the Fire Emblem world and has to adapt to new cultures and challenges. And of course, there are fanfictions that focus on Byleth's growth as a teacher, showing how they develop new teaching methods and inspire their students in ways not shown in the game.
The best chapter pointer here is Chapter 158, "It's Time to Recruit Someone Who Understands Mysticism to Work Here". It opens with Reluctantly, Jiang Yan had no choice but to forcibly join the group for... and closes on we're just very close friends." Sister Li had a vast number of followers....
Chapter 159 is the strongest chapter-level answer because it starts from Seeing the red light of the camera turn on, Su Yinwan looked at the... and follows through on Shang Shaobai, who was browsing through files, received a call from his....
If you want the clearest chapter reference, go to Chapter 127. Early on, Witnessing Jiang Li leave with a bucket, Jiang Yan refused to admit...; later, the chapter leans on Otherwise, how would he ever show his face in the Capital again?"....
If you want the clearest chapter reference, go to Chapter 130. Early on, This task, the first one, should have been his in the bag.; later, the chapter leans on However, just as he was about to get out of the water and take a short....
If you want the clearest chapter reference, go to Chapter 163. Early on, Su Yinwan entered a small room, guided by a staff member.; later, the chapter leans on Inside, there was only one sofa, and she walked over to it as directed by....
If you want the clearest chapter reference, go to Chapter 157. Early on, It was already the last day of Flash Change in his dream.; later, the chapter leans on His good score had successfully surpassed Jiang Li, making him first in....
If you want the clearest chapter reference, go to Chapter 124. Early on, Since there were too many points cards inside Jiang Li's barrel, Director...; later, the chapter leans on However, Jiang Li merely lifted her eyelids and said indifferently, "No....
The best chapter pointer here is Chapter 142, "From Enemy to Best Friend?!". It opens with The ingredients for making Buddha Jumps Over the Wall were still on their... and closes on Wen Jiaojiao immediately lit up and stepped forward to hug Jiang Li's arm..
If you want the clearest chapter reference, go to Chapter 128. Early on, Still hungover, Huo Ziyang had just awakened from a blurry dream when his...; later, the chapter leans on He clicked his tongue in annoyance and picked up the phone..
The best chapter pointer here is Chapter 172, "Shang Shaojing is Here Too?!". It opens with Not only Shu Yan, but the entire internet was shocked when they saw Su... and closes on Where's the chaotic scene I was anticipating?.