Church teaching says nothing about the time of 3 a.m. However, in popular culture it has become known as the “devil’s hour.” This is because Gospel tradition reports that Jesus died at 3 p.m., and so—because the devil likes to mock God—the inverse hour of 3 a.m. is considered the time the devil chooses to manifest most forcefully in the world. Some also claim that due to the large amount of sin committed at 3 a.m. the Communion of Saints often awakens individuals at this time in order to prompt them to pray for others.
All of this, obviously, should be taken with a large grain of salt. None of these popular notions are deeply rooted in Catholic tradition, nor do they have wide acceptance.