The correct answer is A. authoritatively.
The teacher warned the student once for all that no mischief shall be tolerated in the class. This means that the teacher is giving the student a final warning and that any further mischief will not be tolerated. The teacher is speaking in an authoritative manner, which means that they are speaking in a way that shows that they are in charge and that they expect the student to obey them.
The other options are not as accurate. Option B, finally, is not as accurate because it does not convey the sense of authority that is present in the original sentence. Option C, angrily, is not as accurate because it does not convey the sense of finality that is present in the original sentence. Option D, coldly, is not as accurate because it does not convey the sense of seriousness that is present in the original sentence.
In conclusion, the correct answer is A. authoritatively.