Is it permissible to impose a financial fine as a punishment on students absent from classes?

It is not permissible to impose a financial penalty on an absent student, because that is a discretionary punishment (ta'zeer) involving money, and the default rule concerning it is prohibition unless authorized by the Imam (ruler) or his representative. However, if the school provides a monthly allowance, then it is permissible to deduct an amount corresponding to the days of absence, provided that the allowance is conditional upon the student's regular attendance.