Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.125A.

One should do one’s best to make supplications during the last moments (or hours) of Jumu’ah.

‘Abdullah ibn Salam relates: “I said, and the Messenger of Allah was sitting: ‘We find in the Book of Allah that on Friday there is an ‘hour’ in which, if a believing slave prays to Allah for something, his prayer is (indeed) accepted and he is granted what ever he prays for.’ The Messenger of Allah pointed toward me and said: ‘Or part of an hour.’ I said: ‘You have spoken the truth: or part of an hour.’ I asked: ‘What hour is it?’ He replied: ‘The last hour of the day.’ I remarked: ‘That is not a time of salah?’ He responded: ‘Certainly [it is]; if a believing slave offers salah and then sits, he will not be sitting, save due to the salah, and he will be in salah.”‘ This is related by Ibn Majah.

Abu Sa’id and Abu Hurairah report that the Messenger of Allah said: “On Jumu’ah there is a time that if a believing slave asks Allah during it for some good, [Allah will definitely] give it to him, and that time is after the ‘asr salah.” This is related by Ahmad. Al-‘Iraqi calls it sahih.

Jabir reports that the Messenger of Allah said: “The day of Jumu’ah has twelve hours, and during one of the hours, you will not find a Muslim slave [of Allah] asking Allah for something, but that He will give it to him. Seek it in the last hour after the ‘Asr salah.” This is related by anNasa’i, Abu Dawud, and by al-Hakim in al-Mustadrak, and he calls it sahih according to Muslim’s criteria. Ibn Hajar says that its chain is hasan.

Abu Salamah ibn ‘Abdurrahman reports that some companions of the Prophet gathered and mentioned the “hour on Jumu’ah.” They left and did not differ on the fact that it is the last hour of Jumu’ah. This is related by Sa’id ibn Mansur in his Sunan and al-Hafiz Ibn Hajar calls it sahih.

Ahmad ibn Hanbal says: “Most of the hadith concerning the hour in which the supplication is always responded to state the hour to be after the ‘asr prayer, and some state it to be after the sun passes the meridian.”

There is a hadith recorded by Muslim and Abu Dawud which states that Abu Musa heard the Messenger of Allah say concerning the special hour on Jumu’ah: “It is between the time that the imam sits [i.e., upon the pulpit] and the time that the salah is completed.” All the same, this particular hadith is defective because its chain is broken and it is mudtarib.