What Is the Best Dhikr  on Friday?
Question

Are there any authentic hadiths/sunnahs regarding which specific surahs, supplications, phrases etc., we should recite every Friday, and how many times on a Friday we should recite them?
Praise be to Allah.Virtues of Friday
Friday is one of the blessed days on which it is mustahabb (encouraged) to remember Allah, may He be exalted, a great deal in general terms.
Allah, may He be exalted, says (interpretation of the meaning):
“And when the prayer has been concluded, disperse within the land and seek from the bounty of Allah , and remember Allah often that you may succeed.” [Al-Jumu’ah 62:10]
Dhikr on Friday
Adhkar that are mustahabb on other days are even more mustahabb on Friday, because of the virtue of this day.
An-Nawawi (may Allah have mercy on him) said:
“You should understand that every dhikr that may be recited on days other than Friday may be recited on Friday too, and it is more encouraged to remember Allah a great deal on this day than on other days.” (Al-Adhkar, p. 71)
Among the most important adhkar are the adhkar for morning and evening . For more information about the time when they are to be recited, please see the answer to question 22765 .
Best dhikr on Friday
With regard to specific adhkar [on Friday]:
·        Sending a great deal of blessings upon the Prophet (blessings and peace of Allah be upon him)
Aws ibn Aws said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “One of the best of your days is Friday. On it Adam was created, on it he died, on it the Trumpet will be blown and on it all creatures will swoon. So send a great deal of blessings upon me on that day, for your blessings will be shown to me.”
They said: O Messenger of Allah, how will our blessings be shown to you when you will have disintegrated? He said, “Allah, has forbidden the earth to consume the bodies of the Prophets.” (Narrated by Abu Dawud (1047), an-Nasai (1374) and Ibn Majah (1085). Classed as sahih by al-Albani in Sahih Sunan Abi Dawud (4/214); he said: Its isnad is sahih according to the conditions of Muslim. It was also classed as sahih by Ibn Hibban and an-Nawawi.”
·        Reciting (or reading) Surat al-Kahf
Abu Sa‘id al-Khudri (may Allah be pleased with him) said that the Prophet (blessings and peace of Allah be upon him) said:  “Whoever recites (or reads) Surat al-Kahf on Friday , he will be granted light from one Friday to the next.” Narrated by al-Hakim in al-Mustadrak (2/368). He said: This is a hadith of which the isnad is sahih, although they [al-Bukhari and Muslim] did not narrate it. It was classed as sahih by al-Albani in Irwa al-Ghalil (3/93).
·        One should be keen to constantly call upon Allah [du`a] throughout the day on Friday.
Abu Hurayrah that the Messenger of Allah (blessings and peace of Allah be upon him) mentioned Friday, and said: “In it there is a time when, if a Muslim happens to be standing and praying at that time, asking Allah, may He be exalted, for something, He will give it to him” – and he gestured with his hand to indicate how short that time is. (Narrated by al-Bukhari (935) and Muslim (852)
When to make du`a on Friday 
There are many views concerning the definition of that time, the strongest of which are two views, as was explained by Ibn al-Qayyim (may Allah have mercy on him), who said: The most likely of these views to be correct are two which are referred to in the proven hadiths; one of them is more likely to be correct than the other.
1.     The first view is that this time is from when the imam sits [on the pulpit] until the prayer is over . The evidence for this view is the report narrated by Muslim in his Sahih from Abu Burdah ibn Abi Musa, that Ibn `Umar said to him: Did you hear your father narrate anything from the Messenger of Allah (blessings and peace of Allah be upon him) concerning the hour (time when du`as are answered) on Friday? He said: Yes, I heard him say: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “It is between the time when the imam sits [on the pulpit] until he finishes the prayer.”
·        The second view is that it is after `Asr , and this is the view which is more likely to be correct. It is the view of ‘Abdullah ibn Salam, Abu Hurayrah, Imam Ahmad, and others. The evidence for this view is the report narrated by Ahmad in his Musnad from Abu Sa‘id and Abu Hurayrah, that the Prophet (blessings and peace of Allah be upon him) said: “On Friday there is a time when, if a Muslim happens to ask Allah, may He be glorified and exalted, for something good, He will give it to him. That time is after ‘Asr.”
Abu Dawud and an-Nasai narrated from Jabir that the Prophet (blessings and peace of Allah be upon him) said: “Friday is twelve hours, when no Muslim asks Allah, may He be glorified and exalted, for anything but Allah, may He be glorified and exalted, will give it to him. Seek it at the end of the time after ‘Asr.”
This is the view of most of the early generations (salaf), and it is supported by most of the hadiths.
The next strongest view is that it is the time of prayer.
The other views have no evidence to support them.
In my view, the time of prayer is also a time when there is strong hope of du`as being answered, for both of them are times when du`as are answered. Even though the time referred to in the hadith is the last hour after `Asr, because it is a specific time of the day that cannot be brought forward or put back, as for the time of the prayer, it is connected to the prayer and may be brought forward or put back, because the gathering of the Muslims, their prayer and their humble beseeching of Allah, may He be exalted, have an impact on the supplication being answered. So the time when they gather is a time when it is hoped that supplications will be answered. Thus all the hadiths may be reconciled and we understand that the Prophet (blessings and peace of Allah be upon him) urged his ummah to call upon Allah and beseech Him at these two times.” (Zad al-Ma'ad (1/377-382)
An-Nawawi (may Allah have mercy on him) said:
“The scholars of the earlier and later generations differed concerning this time, and there are many views that are widely known among the Muslims. I have compiled all the views that mentioned it in Sharh al-Muhadhdhab, and explained who expressed these views, and that many of the Companions were of the view that it is after ‘Asr. What is meant by standing praying is waiting for the prayer, because the one who is waiting for the prayer is in a state of prayer.” (Al-Adhkar, p. 144)
And Allah knows best.