Sylvleth

Sylvileth is the non-binary ship between Byleth Eisner and Sylvain Jose Gautier from the Fire Emblem fandom.

Canon
Byleth meets Sylvain at the officers academy at the monastery, if they picks the Blue Lions house, he will instantly be Byleth class. However if Byleth chooses the Golden Deer house or the Black Eagle house he wont be in their class and will face them at the end of the first month, then Byleth can still recruit him, before the 5 year time-skip.

The two can reach a A level support. In their first support Byleth see Sylvain breaking with a girl and blames him for breaking the girl heart and for being a skirt-chaser .Then in their second support he explain to them that the girls that are whith him are only for his crest and not himself and that they don't truly love him but whant to use him to have a child with a crest and gain the nobility, he also express his hate of how his crest influate his life and his jalousie of Byleth because they had grow up without knowing they had a crest he after said it was a joke ant that dark and brooding nobles attracts ladys. Their third support take place after a battle where Sylvain was injured protecting Byleth, he said is glad to did it despite he still being jealous of them, he talk about his brother's hate for him and Byleth empathize with him, he then express that Byleth showed another way to lived and he's glad to know them. If Byleth is female, then, they can marry, before the final boss, if the player gets A level support with Sylvain, Byleth will visit her father's grave and take out the ring that he gave her, his words will echo, of her farther telling her to give the ring to a person that Byleth loved as much as Jeralt loved his wife, if the player chooses Sylvain after the battle the two will reunited at the godess tower, he will propose to marry her and she will accept. They will wed after the war.

Azure Moon
If Byleth chose the Blue Lions Sylvain will be one of their student since the begening. After the time skip they reunite along the others Blue Lions at the monastery. They will fight together for the kingdom. After the war Sylvain becomes the new Margrave of Gautier and Byleth becomes the new Archbishop if Byleth archive a S support with him they will marry.

Crimson Flower
On Crimson Flower Byleth sides with Edelgard and the empire.

If Sylvain wasnt recruited before the time skip he will fight against the empire alongside his king Dimitri at Tailtean Plains. If female Byleth battles him, he expresses regret for not having tried to woo her five years ago. He will die during the battle.

If he was recruited before the time skip, Sylvain will abandon House Gautier, accepting a commission to be an Imperial Army general, believing in Byleth more than he does in his own country. After the war he becomes the new leader of the House Gautier. If Byleth marries him she will help him to rebuild the northern Fódlan, after this they will work to end the differentiation of treatment between the person with a crest and those without one, they will finaly have many children.

Verdant Wind/Silver Snow
If Sylvain wasnt recruited before the time skip he won't appare in the Silver Snow route and will fight at the Second Battle of Gronder Field againts the empire and the alliance (Byleth's side) in the Verdant Wind route. If he survive during the battle his fate is left unknow and has probably died after the fight.

If he was recruited before the time skip he joins the monastery and fight alongside Byleth and the Church (and the alliance in Verdant Wind) againts the empire. After the war Sylvain becames the new Margrave Gautier and Byleth becames the ruler of United Kingdom of Fódlan, if they wed they will have many children.

Fanon
The most popular version of this ship is the variant with female Byleth. This paring is quite popular since Sylvain is available in all routes and can be recruited in the early game if Byleth is female (even if the Blue Lions wasnt choosen). Due to the fact that in their paired ending (in non-Azure Moon routes) it's said that they have children many fanarts show them with their kids. Some fanarts represent them in their summer alts from Fire Emblem Heroes. Many fanfictions take place after the game and describe their life with their family. Some of them explore Sylvain traumas.

A popular joke in the fire emblem three houses fandom is that outside the Azure Moon route, Sylvain betrayed his family, kingdom and friends for a girl.

The version of this ship with male Byleth exist but is rare.

Fandom
FAN FICTION

Sylvain Jose Gautier/Byleth tag on A03

TUMBLR

Sylveth posts on Tumblr

Trivia

 * If Byleth didn't chose the Blue Lions house and is female Sylvain will immediately accept a transfer to her class from as early as Chapter 2, regardless of her current stats.