Heat vegetable oil in a deep fryer or large saucepan to 350 degrees F (175 degrees C).

Combine chicken, Cheddar cheese, ranch dressing, butter, and hot sauce in a bowl. Scoop about 1 tablespoon of chicken mixture onto the center of each wonton wrapper; fold wontons in half and press to seal. Arrange wontons on a baking sheet and freeze for 5 to 10 minutes.

Lower wontons carefully into the hot oil in batches. Fry until golden brown, about 2 to 3 minutes. Transfer to a paper towel-lined plate to drain. Repeat with remaining wontons.