بِسۡمِ ٱللَّهِ ٱلرَّحۡمَٰنِ ٱلرَّحِيمِ
Purpose of Sleep
[78:9] And have made your sleep as a thing for rest.[25:47] And it is He Who makes the night a covering for you, and the sleep (as) repose, and makes the day Nushur (i.e. getting up and going about here and there for daily work, etc. after one's sleep at night or like resurrection after one's death).
Sleep is a kind of Temporary Death
[39:42] It is Allah Who takes away the souls at the time of their death, and those that die not during their sleep. He keeps those (souls) for which He has ordained death and sends the rest for a term appointed. Verily, in this are signs for a people who think deeply.[6:60] It is He, Who takes your souls by night (when you are asleep)
Sleeping Less at Night
[51:17] They used to sleep but little by night [invoking their Lord (Allah) and praying, with fear and hope].
Glorifying ALLAH azwajal when awaking
[52:48] Glorify the Praises of your Lord when you get up from sleep.The Messenger of Allah (ﷺ) would take a nap at midday, so that this siesta would give him strength to pray qiyaam al-layl (voluntary prayers at night).
“قيلوا فإن الشياطين لا تقيل”
The Messenger of Allah (ﷺ) would say: “Take a nap at midday, for the Shaytaan does not take a nap at midday.” [Narrated by at-Tabaraani in al-Awsat, 28; classed as hasan by al-Albaani in as-Saheehah, 1647].
Salaf used to sleep forenoon and sometimes afternoon, they pray Jumma earlier and sleep after Jumma
We used to offer the Jumua prayer with the Prophet (ﷺ) and then take the afternoon nap.
[Sahih al-Bukhari 940, 941, 5403]
Imam Bukhari [رحمه الله] in his Adab Al-Mufrad has a separate chapter on midday naps. (https://sunnah.com/adab/52)
Narrated Thumama:Anas said, "Um Sulaim used to spread a leather sheet for the Prophet (ﷺ) and he used to take a midday nap on that leather sheet at her home." Anas added, "When the Prophet (ﷺ) had slept, she would take some of his sweat and hair and collect it (the sweat) in a bottle and then mix it with Suk (a kind of perfume) while he was still sleeping. "When the death of Anas bin Malik approached, he advised that some of that Suk be mixed with his Hanut (perfume for embalming the dead body), and it was mixed with his Hanut. [Sahih al-Bukhari 6281, 6283]
Benefit of Not sleeping after Fajr
Sakhr bin Wada'ah Al-Ghamidi (May Allah be pleased with him) reported:
The Messenger of Allah (ﷺ) said, "O Allah! Bless my people in the early part of the day (morning). Whenever he dispatched a detachment or an army-unit, he would dispatch it at the beginning of the day (soon after dawn). The narrator, Sakhr (May Allah be pleased with him) was a merchant, and he used to send off his merchandise at the beginning of the day. So his trade flourished and he made a good fortune.
[Riyad as-Salihin » The Book of Etiquette of Traveling: 957]
[At-Tirmidhi and Abu Dawud].
Is it not okay to sleep after Fajr?
If a person sleeps at this time to gain strength to do his work, there is nothing wrong with this, especially if it is not easy for him to sleep at any other time of the day.Ibn Abi Shaybah reported in his Musannaf (5/223, no. 25454) from the hadeeth of Abu Yazeed al-Madeeni who said: “Umar came to Suhayb one morning and found him sleeping, so he sat down until he woke up. Suhayb said: ‘The Ameer al-Mu’mineen is sitting in his place and Suhayb is sleeping!’ ‘Umar said to him: ‘I did not like to disturb your sleep that could be beneficial for you.’”
https://islamqa.info/en/answers/2063/sleeping-after-fajr-and-asr
Sh. Ibn ‘Uthaymīn [رحمه الله] said; "Sleeping is a blessing from Allāh as it renews energy and cures tiredness." [Tafsīr Juzz ‘Amma (p. 22) of Ibn ‘Uthaymīn]
Ibn al-Qayyim [رحمه الله] said: "Sleeping too much kills the heart, makes the body heavy and wastes time." [Madārij as-Sālikīn (v. 1 p. 453)]
Ibn al-Qayyim [رحمه الله] said: "The best times to sleep are at the beginning of the night and in the middle of the day." [Madārij as-Sālikīn (v. 1 p. 459)]
Ibn al-Qayyim [رحمه الله] said: "To achieve eight hours of sleep at night is good - not more." [Madārij as-Sālikīn (v. 1 p. 460)]
Ibn al-Qayyim [رحمه الله] said: "To sleep 8 hours during the night (4) and day (4) is best." [Zād al-Ma’ād (v. 1 p. 155)]