Tophuki

Tophuki is a Femslash ship between Toph Beifong and Suki in the Avatar: The Last Airbender series.

Canon
Toph and Suki first met while they were traveling in a group through the Serpent's Pass. At one point, Toph fell into the water and she could not swim. Sokka yelled that he was about to jump into the water and save her but Suki went in instead. Suki managed to grab Toph and pull her to the surface. Being blind, Toph thought that she was in Sokka's arms and thanked him for saving her and kissed Suki on the cheek. Suki smiled politely and explained that it was her and not Sokka. Toph laughed and gave Suki permission to let her drown.

Suki ended up dating Sokka whom Toph also had a crush on. They would not see each other for a long time until Sokka and Zuko managed to rescue Suki from the Boiling Rock. Toph did not seem to mind having Suki in the group. At one point, Sokka made a sand sculpture of Suki's head which nobody recognized. It was so bad that Toph gave Suki permission to break up with Sokka over it. Later, Toph and Suki took down a Fire Nation airship fleet along with Sokka. Afterwards, they made fun of Ozai who had just lost his bending to Aang. Suki called him the king of guys who don't win and Toph told Suki to leave the nicknames to her and Sokka.

Fanon
Tophuki has a small amount of shippers in the Avatar fandom. It is almost entirely based on the fact that Toph kissed Suki on the cheek at one point, even if it was an accident. That kiss is well known and it is also known for being the only same-sex kiss to be seen in both series. Many fans point out the fact that Suki smiled after the kiss and did not seem to be bothered by it.