Unfortunately, it is practically impossible to answer such a broad question with specifics, but we'll try without going into the detail necessary to provide a comprehensive answer.
First, we need to define the word and concept of "authority." Generally speaking, authority is given or granted to individuals or institutions by another or others. Even usurpers and tyrants who seize power through violence still need the submission of those whom they seek to serve them, else they would have no power at all. Consider this even from a positive perspective, as when those who are oppressed rebel and seek to lift the burden of tyranny, such as with the American and French Revolutions. Where did those who rebelled against their monarchies obtain *their* "authority" to do so?
Where does the Earth get its "authority" to revolve in a fixed orbit around the Sun? Or rotate upon its axis once every 24 hours? One could argue that such "authority" comes from the unchangeable "laws" of physics — but who, or what, created those "laws"?
Yet another question: Who is greater; the one who has been given "authority" or the one who grants or gives that authority? For example: through force, Alexander the Great expanded the borders of his empire far beyond any other that came before it. Could Alexander have accomplished this alone, as one man without an army of soldiers willing to obey his commands? He was arguably one of the most powerful conquerors in human history, possessing nearly absolute control ("authority") over an area that spanned multiple continents. Yet, for all that "authority" could Alexander cause it to rain on his command? Could he make a single blade of grass grow instantly? Could he heal the sick with the touch of a hand? Could he raise the dead with a spoken word? Could he walk on water?
So, back to "What is God's authority?"
In short, "GOD" created the entire universe, and every last particle contained in it, including the ones that make up every human that has ever lived. We are literally, though indirectly, "the work of His hands." Our very lives are gifted to us by His will and good pleasure. We are told that a potter can make two vessels with the same clay as he sees fit — one to honor and another to "dishonor" (i.e. one can be a king's chalice, another can be a chamber pot).
We grant no "authority" or ability to God. We are powerless, helpless, unable to disobey even the most basic "law" of physics. To Him and Him alone belong all right and "authority" inherent in the Creator and Emperor of everything that is and ever will be.
This leads us to the unavoidable question, if GOD has such "Absolute Authority" then why do Satan and evil exist, and why can we choose between right and wrong? The natural question and answer have to do with the PERMISSION OF EVIL.
God is permitting Satan and evil to exist for the present. But when the words of the Lord’s Prayer, “Thy kingdom come, thy will be done, on earth as it is in heaven,” are fulfilled, then all enemy dominions, authorities, powers will have been destroyed (1 Cor. 15: 24-27).
