The serpent king in European legend said to kill with a single glance is the basilisk.
Medieval and Renaissance European tradition portrayed the basilisk as a small but exceptionally deadly reptile, sometimes described as a serpent crowned with a crest. Its name is linked to the Greek basilískos, meaning “little king,” which explains the title “serpent king.” Legends credited it with a lethal gaze, poisonous breath, or both.
Accounts varied considerably. Some writers treated the basilisk as a distinct snake, while others merged its characteristics with the cockatrice, a rooster-headed dragon or serpent-like creature. Natural-history writers also repeated reports that the creature could be born from an unusual egg, reflecting folklore rather than zoological observation.
The basilisk is often confused with Medusa, whose gaze turns people to stone in Greek mythology. Both creatures are associated with deadly eyes, but Medusa is a Gorgon and a mythological woman, whereas the basilisk is a European legendary reptile. “Gorgon” is therefore a broader or different category, not the canonical answer here.