Sylkior

Sylkior is the family/poly ship between Loki, Sylvie Laufeydottir, and Thor Odinson from the Marvel Cinematic Universe fandom.

Canon
Loki and Thor are brothers with a long history, and they shared that history up until 2012 when Loki's timeline deviated. The version of Loki in the Sylkior ship is the one who deviated from the timeline in 2012, so Thor lived out a future with a version of Loki who died, and which Loki from 2012 did not personally experience. However, Loki is aware of that intended future, as he witnessed footage of it in the Time Theater in the TVA. Loki is interested in returning to his timeline (and to Thor), although the TVA will not allow it. Thor is unaware that a version of his brother is still alive.

Loki and Sylvie are canon romantic interests who currently share mutual feelings for each other. They are also variants of each other from different timelines, and they share a temporal aura (a soul).

Sylvie and Thor have never met in canon. Sylvie presumably had a variant of Thor as her brother when she was a child on Asgard, but it's unconfirmed if she remembers him.

Fanon
Since Loki and Sylvie are variants of each other, many fans believe that Thor would embrace Sylvie as a family member. The three are also shipped romantically.

Fans began taking an interest in the ship following episode 3 of the Loki series, and the term Sylkior came into usage on social media. As Loki and Sylvie bonded on Lamentis in episode 3, fans began to ship Loki and Sylvie both romantically and platonically as being like long-lost twins, and fans began to imagine their relationship with Loki's brother Thor as well.

Platonic fanart:
 * Family portrait by @mjarmerchant on Twitter, July 5, 2021.
 * I love them & want them to be a big awkward family by @solidafg on Twitter, July 5, 2021.
 * Sibling bonding time by @MysiePereira on Twitter, June 30, 2021.
 * Siblings? Siblings by @octisquad on Twitter, June 29, 2021.
 * Sylvie meets Thor by @octisquad on Twitter, June 29, 2021.
 * Sleeping by @sensoriumz on Twitter, July 2, 2021.
 * Another! by lousysharkbutt on Tumblr, June 30, 2021.

Romantic fanart:
 * "Wow Loki you were right! Your Thor is indeed hot" by deraniel on Tumblr, July 1, 2021.
 * Sylkior in bed (semi-NSFW but not explicit) by @ponderosa121 on Twitter, July 5, 2021.

Fanedits:
 * Meme "This is my boyfriend Loki, & this is Loki's boyfriend Thor"

Variations

 * Thorki, the ship between Thor and Loki
 * Sylki, the ship between Sylvie and Loki