What is the ruling of Sharia on imposing a financial fine on students who are late for congregational prayers, and doubling this fine if payment is delayed?

Taking money from someone who slept through a prayer, or missed the congregational prayer at the mosque, is a form of financial chastisement (ta'zir bi al-mal), which is impermissible for two reasons:

First: Chastisement (ta'zir) is applied to sins for which no specific punishment has been prescribed by Sharia. However, someone who misses a prayer due to sleep is not considered disobedient, as per the Hadith: "There is no negligence in sleep; negligence is only in wakefulness. So if one of you forgets a prayer or sleeps through it, let him pray it when he remembers it." Furthermore, attending congregational prayer in the mosque is not an individual obligation (wajib 'ala al-a'yan) according to the majority of scholars.

Second: Financial chastisement (ta'zir bi al-mal) for sins is not legislated according to the majority of scholars. And even if it were permissible, it is the responsibility of the ruler (wali al-amr) to implement it.