Paralogue quests in Fire Emblem Fates are extra missions for bonus EXP and characters. You will get a couple by default but the rest will need to be unlocked. Check out this guide to figure out How To Unlock Paralogue Quests In Fire Emblem Fates!
How To Unlock Paralogue Quests In Fire Emblem Fates
The way you unlock the extra Paralogue missions is by getting S rank relationships with your characters. When you get an S rank with your main character, they get married and have a kid which becomes and Paralogue mission. In order to get S rank you will have to have units fight together in Combat. They don’t HAVE to be paired up but this is the easiest way to guarantee they will fight together. At the same time, placing them next to each other could result in two attacks instead of one. It really will come down to the type of Battle you are doing and which characters you bring. I will tell you which ones I have unlocked so far and how I got them.
Fire Emblem Fates Birthright Paralogue Quests Unlock Guide
Fire Emblem Fates Conquest Paralogue Quests Unlock Guide
Paralogue Missions 2-5 are the same on both games because you get those units on both games.