This list of mythical creatures that begin with this letter and I am constantly gathering information from each continent, and is continually being updated.
Teumessian Fox (Greek)
It was said that the Teumessian fox had been sent by the gods (perhaps Dionysus) to prey upon the children of Thebes as a punishment for a national crime. Creon, then-Regent of Thebes, set Amphitryon the impossible task of destroying this beast. He discovered a supposedly perfect solution by using the magical dog Laelaps, who was destined to catch everything it chased, to catch the Teumessian fox.
Zeus, faced with an inevitable contradiction due to the paradoxical nature of their mutually excluding abilities, turned the two beasts into stone. The pair were cast into the stars and remain as Canis Major (Laelaps) and Canis Minor (Teumessian Fox).