One can read the Quran at any time during the day or the night as long as one is in a state of ritual purity.

 

It is prohibited to offer supererogatory prayers during those times according to the hadith of the Prophet (peace be upon him) in which he is reported as: “forbidding praying after the morning prayer until the sun had risen, and praying after `Asr until the sun had set.” (Abu Dawud)

 

Scholars interpreted the word ‘praying’ to refer to supererogatory prayer which does not have a legal cause. An example of nafl prayers which has a legal cause is praying two rak`ahs upon entering a masjid which is recommended any time. This is according to the view of the Shafi`i scholars.

Allah Almighty knows best.