What is the ruling on one who misses performing the Fajr prayer at its prescribed time due to not getting enough sleep, which makes him unable to wake up upon hearing the Adhan, especially in summer when the period between Isha and Fajr is short?

If sleep overwhelms you and you are unable to wake up, there is no sin upon you, and you must pray immediately upon waking. However, if you wake up after the time for the prayer has begun and you hear the call to prayer (adhan (definition)), then you must promptly get up and perform the prayer; otherwise, you would be sinful. There is no excuse for you to continue sleeping after waking up once the prayer time has begun. Rather, you must rise for the prayer, and then you may sleep as much as you wish afterward.