✅Answer: 'Qaylulah' in terms of language refers to a short nap taken around midday.

1 جعفربن مُحَمَّدٍ عن أَبِيه عن النَّبِيِّ أَنَّ أَعْرَابِيّاً أَتَاهُ فقال يا رَسُول اللَّه إِنِّي كُنْتُ رَجُلًا ذَكُوراً فَصِرْتُ نسيا فقال لَهُ رَسُولُ اللَّه لَعَلَّكَ اعْتَدْتَ الْقَائِلَةَ فَتَرَكْتَهَا قَالَ نَعَمْ فَقَالَ لَهُ رَسُولُ اللَّه فَعُدْ يَرْجِعْ إِلَيْكَ حِفْظُكَ إِنْ شَاءاللَّهُ

📚Qurb al-Isnad 34

Imam Baqir (peace be upon him) said: 'A bedouin came to the Messenger of Allah (peace be upon him and his family) and said: 'I was a man of good memory but I have become forgetful!''

The Prophet said to him: 'Perhaps you were accustomed to the qaylulah nap and you have stopped it!'

He said: 'Yes!'

So the Prophet said to him: 'Return to the qaylulah nap so that your memory returns to you, God willing!'

2 وَ رُوِیَ قِیلُوا فَإِنَّ الشَّیْطَانَ لَا یَقِیلُ.

📚Faqih, Vol. 1, p. 503

Saduq said: 'It is narrated: Take a qaylulah nap, for Satan does not take a qaylulah nap!'

3 قال الباقر النَّوْمُ أَوَّلَ النَّهَارِ خُرْقٌ و الْقَائِلَةُ نِعْمَةٌ و النَّوْمُ بَعْدَ الْعَصْرِ حُمْقٌ و النَّوْمُ بَيْنَ الْعِشَاءَيْن يَحْرِمُ الرِّزْقَ

📚Faqih, Vol. 1, p. 502

Imam Baqir (peace be upon him) said: 'Sleeping at the beginning of the day is ignorance, the qaylulah nap is a blessing, sleeping after Asr is foolishness, and sleeping between Maghrib and Isha deprives one of provision!'

4 قال أَبوالحسن قِيلُوا فَإِنَّ اللَّهَ يُطْعِمُ الصَّائِمَ و يَسْقِيهِ فِي مَنَامِه

📚Kafi, Vol. 4, p. 65

Imam Kadhim (peace be upon him): 'Take a qaylulah nap, for God feeds and gives water to the fasting person in his sleep!'

5 أَبِي عبدالله عن أبيه قال: قال رَسُولُ اللَّه تَعَاوَنُوا بِأَكْلِ السَّحُورِ عَلَى صِيَامِ النَّهَارِ و بِالنَّوْمِ عِنْدَ الْقَيْلُولَةِ عَلَى قِيَامِ اللَّيْل

📚Tahdhib, Vol. 4, p. 199

The Messenger of Allah (peace be upon him and his family) said: 'Seek help for the day's fast by eating suhoor, and seek help for the night's vigil by taking a midday nap!'

6 عن جعفر بن محمد : فِي حديث طويل في مَقْتَلِ الْحُسَيْنِ إِلَى أَنْ قال ثُمَّ سَارَ حَتَّى نَزَلَ الْعُذَيْبَ فَقَالَ فِيهَا قَائِلَةَ الظُّهْرِ ثُمَّ انْتَبَهَ مِنْ نَوْمِهِ بَاكِياً فَقَالَ لَهُ ابْنُهُ مَا يُبْكِيكَ يا أَبَهْ فَقَالَ يَا بُنَيَّ إِنَّهَا سَاعَةٌ لَا تُكْذَبُ فِيهَا الرُّؤْيَا

📚Amali al-Saduq, p. 131

Imam Sadiq (peace be upon him), in a hadith about the martyrdom of Hussein (peace be upon him), said: 'Then Imam Hussein (peace be upon him) moved until he reached the station of Uthayb and took his midday qaylulah nap there, and then he woke up crying!'

His son said to him: 'O my father, what has made you cry?' He said: 'O my son! This is an hour in which dreams do not lie...'

7 عن الرِّضا في حديث قال:فَإِذَا كانَ نِصْفُ النَّهَار و تَرَكُوا ما كانوا فيه مِنَ الشُّغُلِ و هُوَ وَقْتٌ يَضَعُ النَّاسُ فِيهِ ثِيَابَهُمْ و يَسْتَرِيحُون و يَشْتَغِلُونَ بِطَعَامِهِمْ و قَيْلُولَتِهِمْ فَأَمَرَهُمْ أَنْ يَبْدَءُوا أَوَّلًا بِذِكْرِهِ و عِبَادَتِهِ فَأَوْجَبَ عَلَيْهِمُ الظُّهْرَ ثُمَّ يَتَفَرَّغُوا لِمَا أَحَبُّوا مِنْ ذَلك

📚Ilal al-Shara'i, p. 263

Imam Reza (peace be upon him), in a hadith about the times of prayer, said: 'When midday comes and people leave the tasks they were busy with, and it is a time when people put down their clothes and rest and get busy with their food and their qaylulah nap, God has commanded them to begin by remembering and worshipping Him. So He has made the Dhuhr prayer obligatory upon them at this time, and then they can be free for whatever they like of those tasks!'

8 From Zurarah, he said: 'I said to Abu Abdillah (Imam Sadiq): 'I fast, so I do not take my qaylulah until the sun declines. So when the sun declines, I perform my supererogatory prayers and then I perform the Dhuhr prayer and then I perform the Asr supererogatory prayers and then I perform the Asr prayer and then I sleep, and this is before people pray!'

📚Tahdhib, Vol. 2, p. 247

The Imam said: 'When the sun declines, the time has entered, but I dislike for you to make it a permanent time!'

✅It is clear from the above narrations and others that the qaylulah nap is recommended and has benefits, especially for a fasting person, and its time is recommended after the Dhuhr prayer in hadith 7. However, considering its linguistic meaning of a midday nap and the indication of some narrations like narration 8, it also includes a nap near midday.