There are many Prophetic hadiths reflecting on virtues of reciting surat Al-Kahf during the day and night of Friday. To state just a few of those hadiths, i would like to cite for you the following:
Abu Sa`id A-Khudri (may Allah be pleased with him) said: “Whoever reads surat Al-Kahf on the night of Friday, will have a light that will stretch between him and the Ancient House (i.e., the Ka`bah).” (Reported by Al-Darimi)
The Prophet (peace and blessings be upon him) is reported to have said: “Whoever reads surat Al-Kahf on the day of Friday, will have a light that will shine from him from one Friday to the next.” (Reported by Al-Hakim)
Ibn umar (may Allah be pleased with him) quoted the Prophet (peace and blessings be upon him) as saying: “Whoever reads surat Al-Kahf on the day of Jumu`ah (Friday), a light will shine for him from beneath his feet to the clouds of the sky, which will shine for him on the Day of Resurrection, and he will be forgiven (his sins) between the two Fridays.”
Hence, one may read surat Al-Kahf during the night or the day of Jumu`ah. The night of Jumu`ah starts from sunset on Thursday, and the day of Jumu`ah ends at sunset. Therefore the time for reading this surah extends from sunset on Thursday to sunset on Friday.
Imam Al-Mannawi quotes Al-Hafiz ibn Hajar as saying in his book Al-Amali: “In some narrations, it is said that ‘the day of Jumu`ah’, and in some others it said that ‘the night of Jumu’ah’. They may be reconciled by saying that what is meant is the day which includes the night and vice versa.” (Fayd al-Qadir, 6/199)
Imam Al-Mannawi also says: “It is recommended to read surat Al-Kahf during the day or night of Jumu`ah, as Imam Ash-Shafi`i (may Allah have mercy on him) stated.” (Fayd al-Qadir, 6/199)”