Pardon this back-to-front approach, but with regard to the question of what "authority" in Colossians 2:10 refers to, I am going to start with C - Another possibility (that is, other than the Church, or things outside of the Church).
There is authority, and there is Supreme Authority.
So, yes, there is another possibility to be considered, for without question, there is authority in the Church, and authority outside of the Church. My point is that the text in question is dealing with Supreme Authority, not authority with a lower case 'a' that can be seen all over the place, both inside the Church and outside of the Church.
If that can be established from the text, then no more needs to be said.
The text is set within the context of how Christians are protected from being beguiled, that is, deceived. They who have received Christ by faith are to walk in him, rooted and built up in him. The risen Christ has been portrayed to them as having "all the treasures of wisdom and knowledge". Indeed, "all the fullness of the Godhead dwells bodily in Him". The two Greek words chosen by Paul for 'dwelling' and 'Godhead' are not the lesser words meaning 'divine' and 'temporary abode' but the strongest ones possible to convey that Christ is God. Now, what kind of authority does God have and - therefore - what kind of authority does Christ have? Is it authority, or Supreme Authority? This should be self-evident.
So far, there is not even a hint of any kind of authority Christians have. When we read the verse in question, has the matter of the authority of Christians been introduced? Consider two other translations of the whole sentence, which agree with the one preferred in the question:
"For in Him all the fulness of Deity dwells in bodily form, and in Him
you have been made complete, and He is the head over all rule and
authority." N.A.S.B.
"For in him dwelleth all the fulness of the Godhead bodily, and ye are
complete in him, which is the head of all principality and power [the
Greek word rendered 'power' being 'authority'.] The Englishman's Greek New Testament,
Robert Estienne, originally published 1624
When the text speaks of 'him' and 'he', that means the risen Christ. When the text speaks of 'ye' and 'you', those are the Christians. In the text the Christians are stated to have been made complete in Christ, because of his Supreme Authority.
To complete dealing with the 'A' part of the question, it only remains to be pointed out that the risen Christ is King of kings, and Lord of lords, with even demons subject to his authoritative commands (e.g. needing his permission to go into a herd of pigs). Satan is also subject to his authority as shown in how he is cast out of heaven, confined to Earth, then cast into the abysss before, finally, the eternally burning lake of sulphuric fire.) If that isn't Supreme Authority, I don't know what is.
Regarding 'B' - Colossians 2:8 - speaks of Christians not becoming captivated by lying powers pretending to have Supreme Authority, when they do not. They are would-be-usurpers. Christians who are firmly rooted and built up in Christ are protected from such deceptive claims as they remain faithful to the Supreme Authority of Christ.
Therefore 'C' has been shown to be the answer: that 'authority' in Colossians 2:10 means the Supreme Authority of the risen Christ.