What is the ruling on one who delayed their sleep and relied on an alarm clock to wake up for Fajr prayer, but did not hear the alarm and prayed Fajr two minutes before sunrise, relying on a calendar, and is ignorant of how to verify the time of sunrise?

There is no blame on someone who is overcome by sleep and misses the Fajr prayer, after having set an alarm to wake up. This is because they are excused, and the pen has been lifted from the sleeper until they awaken. There is no negligence in sleeping, rather negligence applies to one who does not pray a prayer until the time for the next prayer arrives. This is evidenced by the action of the Prophet (peace and blessings be upon him) and his companions when they overslept and missed the Fajr prayer during one of the campaigns; they prayed it after they woke up. Therefore, whoever oversleeps and misses a prayer, or forgets it, should pray it whenever they remember it. This is with an emphasis on the importance of prayer performed at its due time, as it is the most beloved deed to Allah after faith. A Muslim must take the necessary measures to wake up.