A Gaiden chapter (外伝 Gaiden) or a Paralogue (also known as a Sidequest, particularly in the Japanese version of Fire Emblem Awakening and Side Story in the European version of Fire Emblem Awakening) are side Chapters that require certain conditions to be met in order to play.
Thracia 776-Sacred Stones and New Mystery
This feature was first introduced in Fire Emblem: Thracia 776. Gaiden chapters in these games are denoted by an "x" after the previous chapter's number, such as "17x" or "20x". Most of these gaiden chapters require certain side objectives to be fulfilled in the previous chapter, such as keeping NPCs alive or finishing the previous chapter in a certain amount of turns. The only exceptions to this rule are Chapter 29xE/31xH of Fire Emblem: The Blazing Blade and Chapter 5x of Fire Emblem: The Sacred Stones, both of which are unlocked automatically. These gaiden chapters provide items, recruitable characters, as well as extra EXP for the player's army.
In Fire Emblem: The Binding Blade, each gaiden chapter gives the player a legendary weapon. The player needs to obtain all of the legendary weapons and keep them intact all the way through Chapter 22 to unlock the "true" ending and the last few chapters of the game.
In Fire Emblem: New Mystery of the Emblem, the gaiden chapter conditions are slightly different in that there are 2 of them, but only 1 has to be fulfilled to access the gaiden chapter.
Shadow Dragon features gaiden chapters which involves recruiting brand-new characters that were not in the original Fire Emblem: Shadow Dragon and the Blade of Light. Similar to the gaiden chapters in the previous games, the gaiden chapters in Shadow Dragon are denoted by an "x".
These chapters are only accessible if Marth's army has less than a specific amount of units in his army at the point of the chapter starting. The sole exception being Chapter 24x where the only means to play this chapter is to have Tiki dead and the Falchion is lost.
Fire Emblem Awakening introduced alternative chapters called Paralogues. Unlike previous Gaiden Chapters, these chapters can be completed at any time after they are unlocked. There are 22 Paralogues in Awakening which are divided into 3 different types. Four Paralogues are side stories of the Shepherds helping out villages in Ylisse and protecting Tiki. These are unlocked once certain chapters have been completed. 12 Paralogues are side stories where the Shepherds meets their future children who accompanied Lucina from the future. These are unlocked once a specific female character or male Robin has achieved an S-Support. The last 6 Paralogues are side stories where the Shepherds re-encounter story units who have survived the events of the story. These were initially unlocked once the player reached the Endgame and has downloaded the chapter from SpotPass.
Fire Emblem Fates adopted the Awakening Paralogues and features 22 of them. Only one Paralogue is unlocked by completing a specific chapter. The other 21 Paralogues are achieved once a specific male character, Azura, or Corrin has achieved an S-Support. In these Paralogues, the player can recruit the child units of the parent characters in their army.
Depending on the route the player has picked, only certain Paralogues are available in Birthright and Conquest. Since all parent characters are playable in Revelations, the player is able to access all the Paralogues in that route.
It should be noted that in Birthright, Midori's paralogue cannot be played until after Chapter 15, even if Kaze already has an S-Support. In order for the paralogue to be playable, the Avatar must have an A support or higher with Kaze before the chapter is completed.
Fire Emblem Heroes has Paralogue chapters that are released from time to time which also feature events that lie outside of the main storyline. These generally involve Seasonal Heroes and related festivals, others are side stories involving normal Hero units. Each Paralogue Chapter has three sub-chapters compared to the Main Story which normally has five sub-chapters.
Fire Emblem: Three Houses sees the return of Paralogue chapters, but are tweaked in purpose: they are found in the Battle section of the menu, alerted on the Calendar as a green exclamation mark. Paralogue battles cost a Battle Point. These Paralogue battles are unlocked by having at least one of the required characters recruited. They are first unlocked following the events of Chapter 5.
If Byleth has managed to recruit the required unit that happens to have a Crest, they will be rewarded with a Hero's Relic that is tied to that Crest. If they are just part of Byleth's army under Mission Assistance, the Relic is then lost to Byleth and is out of their reach.
Additionally, much like before, Paralogue Battles are under a time limit. During the Academy Phase, nearly all of the Paralogue battles last until the end of the Pegasus Moon (2/22), excluding Byleth and Sothis' Paralogue, which expires the month before (1/25). During the War Phase, there are Paralogue battles that are either exclusive to a route, or barred from a route.