Answer
Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is makruh to single out the day of Friday for fasting, unless that coincides with a fast which one usually observes, such as a person who fasts alternate days, and a day that he fasts coincides with Friday, or a person who has the habit of fasting on the first or last day of the month, or the middle day of the month.
In his response to the question, Sheikh Muhammad Saleh Al-Munajjid, the prominent Saudi Islamic lecturer and author, stated:
Abu Hurairah (may Allah be pleased with him) reported that: “I heard the Prophet (peace be upon him) say, ‘None of you should fast on a Friday unless he fasts the day before or the day after.’” (Al-Bukhari and Muslim)
The Prophet (peace be upon him) said, “Do not single out the night of Jumu`ah [i.e., Thursday night] from among other nights for praying qiyam al-layl, and do not single out Friday from among other days for fasting, unless it is a fast that one of you regularly observes.” (Muslim)
It was narrated from Juwayriyah bint al-Harith (may Allah be pleased with her) that the Prophet (peace be upon him) entered upon her on a Friday when she was fasting. He asked her, “Did you fast yesterday?” She said, “No.” He asked, “Are you going to fast tomorrow?” She said, “No.” He said, “Then break your fast.” Hammad ibn al-Ja`d said, “I heard Qatadah say, Abu Ayyub told me that Juwayriyah spoke to him and he told her to stop her fast and she did so.” (Al-Bukhari)
Ibn Qudamah said: “It is makruh to single out the day of Friday for fasting, unless that coincides with a fast which one usually observes, such as a person who fasts alternate days, and a day that he fasts coincides with Friday, or a person who has the habit of fasting on the first or last day of the month, or the middle day of the month.” (Al-Mughni, vol. 3, p. 53)
Al-Nawawi said: “Our companions (i.e. the Shafa`is) said: it is makruh to single out the day of Friday for fasting, but if one joins it with the day before or the day after, or it coincides with a day which he habitually fasts, or he vowed to fast the day that his sick loved one was cured, or the day So and so returns, and that day happens to be a Friday, then it is not makruh (Al-Majmu’ Sharh al-Muhadhdhab, vol. 6, p. 479)
Shaykh al-Islam (may Allah have mercy on him) said: “The Sunnah says that it is makruh to single out Rajab for fasting, and it is makruh to single out Friday (for fasting).” (Al-Fatawa al-Kubra, vol. 6, p. 180)
Shaykh Ibn ‘Uthaymeen said: “As for Friday, it is not Sunnah to fast on this day, and it is makruh to single it out for fasting.” (Al-Sharh al-Mumti’, vol. 6, p. 465)
Excluded from this prohibition is one who fasts the day before or after, or if it coincides with days that he habitually fasts, such as one who fasts al-Ayyam al-Beed (the 13th, 14th and 15th of each hijri month), or who has the habit of fasting a specific day such as the Day of ‘Arafat, and it coincides with a Friday.
From this it may be understood that it is permissible for a person who has vowed to fast on the day when so and so returns, for example, or the day when so and so recovers from sickness, to observe that fast if that day happens to be a Friday. (Fath al-Bari by Ibn Hajar)
The same applies to one who has fasts to make up for the missed days of Ramadan. “It is permissible for a Muslim to fast on a Friday to make up a day from Ramadan, even if he fasts the Friday on its own.” (Al-Lajnah al-Da’imah, vol. 10, p. 347)
Similarly, if Ashura or Arafah coincides with a Friday, he may fast because his intention is to fast Ashura or ‘Arafat not to fast on a Friday.
Allah Almighty knows best.
Source: www.islamqa.info