When is the time for a nap (qaylulah), is it before or after Dhuhr prayer, and is it related to verse (58) from Surat An-Nur: "and when you lay aside your garments in the noonday (ẓahirah)"?

Qaylulah is resting before the Dhuhr prayer. Ibn Manzur said: It is resting at midday when the heat intensifies, even if there is no sleep.

It was reported in Sahih Al-Bukhari from Sahl: "We did not take a qaylulah or eat lunch until after the Friday prayer." Al-Mubarakpuri explained this by saying that they would be busy preparing for the prayer, then they would leave and take their qaylulah and eat lunch after the Friday prayer, as compensation for what they missed.

As for the noble verse: "And when you put off your garments [for rest] at noon" (An-Nur:58), what is meant by "noon" is the time of qaylulah, when a person takes off their garments in this situation with their family.