Snake or dragon in Hebrew was made by YHWH Elohim (Gods) It was not a beast of the earth,Genesis 1:24 Then God said, "Let the earth bring forth living creatures after their kind: cattle and creeping things and beasts of the earth after their kind"; and it was so.

Beast of the field is a later making not creation as beast of the Earth.
Genesis 3:1 Now the serpent was more crafty than any beast of the field which the LORD God had made. And he said to the woman, "Indeed, has God said, 'You shall not eat from any tree of the garden '?"