Fasting on Saturdays: Is It Allowed?
Question

What is the ruling on fasting on Saturdays at times other than Ramadan? What if the day of ‘Arafah happens to be on a Saturday?
Praise be to Allah.Singling out Saturdays for fasting
It is makruh to single out Saturday for fasting, because of the report narrated by al-Tirmidhi (744), Abu Dawud (2421) and Ibn Majah (1726) from ‘Abd-Allah ibn Busr, from his sister, that the Messenger of Allah (peace and blessings of Allaah be upon him) said: “Do not fast on Saturdays apart from days when you are obliged to fast. If any one of you cannot find anything other than grape stalks or the twigs of a tree, let him chew it (to make sure that he is not fasting).” Classed as sahih by al-Albani in al-Irwa (960). 
Abu ‘Isa al-Tirmidhi said: 
“This is a hasan hadith. What is makruh in this case is for a man to single out Saturday for fasting, because the Jews venerate Saturday .”
Ibn Qudamah (may Allah have mercy on him) said in al-Mughni (3/52): 
“Our companions said: It is makruh to single out Saturday for fasting … what is makruh is singling out that day. If he fasts another day along with it, then it is not makruh, because of the hadith of Abu Hurayrah and Juwayriyah. If it coincides with a day that a person regularly fasts, it is not makruh.” 
What is meant by the hadith of Abu Hurayrah is the report narrated by al-Bukhari (1985) and Muslim (1144) from Abu Hurayrah (may Allah be pleased with him) who said: I heard the Prophet (peace and blessings of Allah be upon him) say: “No one of you should fast on Friday, unless he fasts (a day) before it or after it.” 
The hadith of Juwayriyah was narrated by al-Bukhari (1986) from Juwayriyah bint al-Harith (may Allah be pleased with her), that the Prophet (peace and blessings of Allah be upon him) entered upon her on a Friday and she was fasting . He said; “Did you fast yesterday?” She said, “No.” He said: “Do you intend to fast tomorrow?” She said: “No.” He said: “Then break your fast.” 
This hadith and the one before it clearly indicate that it is permissible to fast on a Saturday at times other than Ramadan, for the one who fasts the Friday before. 
It is proven in al-Sahihayn that the Prophet (peace and blessings of Allah be upon him) said: “The most beloved of fasting to Allah is the fast of Dawud; he used to fast one day and not the next.” 
In this case it is bound to happen that he will sometimes fast on a Saturday on its own. So it may be understood from this that if Saturday coincides with a day that he habitually fasts, such as ‘Arafah or ‘Ashura’, there is nothing wrong with fasting on that day, even if it is on its own. 
Al-Hafiz stated in al-Fath that an exception to the prohibition on fasting on Friday is made if a person habitually fasts on a certain day, such as ‘Arafah, and it coincides with Friday. 
The same applies to Saturday. We have quoted the words of Ibn Qudamah concerning that above. 
Different scenarios for fasting on a Saturday
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said:  
“It should be noted that different scenarios may apply with regard to fasting on a Saturday. 
1– It may be obligatory, such as observing a Ramadan fast during Ramadan or making it up later on, or observing a fast as expiation (kaffarah), or instead of offering a sacrifice when performing Hajj tamattu’, and so on. There is nothing wrong with that so long as he does not single it out deliberately thinking that there is some virtue in that. 
2– If he fasts on the Friday before, there is nothing wrong with it, because the Prophet (peace and blessings of Allah be upon him) said to one of the Mothers of the Believers who was fasting on a Friday : “Did you fast yesterday?” She said: “No.” He said: “Are you going to fast tomorrow?” She said, “No.” He said: “Then break your fast.” The words, “Are you going to fast tomorrow?” indicate that it is permissible to fast Saturday along with Friday. 
3– If it happens to be one of the days when it is prescribed to fast, such as Ayyam al-Beed (the 13
th, 14th and 15th of each hijri month), ‘Arafah, ‘Ashura, six days of Shawwal for one who has fasted Ramadan, and the ninth of Dhul-Hijjah . There is nothing wrong with that, because he is not fasting because it is Saturday, rather it is because it is one of the days when it is prescribed to fast. 
4– When it happens to be a day when he habitually fasts, such as a person whose habit is to fast alternate days, and the day that he fasts happens to be a Saturday, then there is nothing wrong with it, as the Prophet (peace and blessings of Allah be upon him) said when he forbade fasting one or two days before Ramadan begins: “except a man who (habitually) observes a fast, in which case let him fast.” This is similar. 
5– If he singles it out to observe a voluntary fast for one day only. This is what is forbidden, if the hadith forbidding it is proven to be sahih.” (Majmu’ Fatawa wa Rasail al-Shaykh Ibn ‘Uthaymin, 20:57) 
A number of scholars were of the view that the hadith which says it is not allowed to fast on a Saturday is weak (da‘if), and they deemed it to be odd (munkar). These scholars include Imam Malik, Ahmad, az-Zuhri, al-Awza i, Shaykh al-Islam Ibn Taymiyah, Ibn al-Qayyim, Ibn Hajar and others.
Ibn Baz, Ibn ‘Uthaymin and the members of the Permanent Committee also favoured the view that it is weak.
As the hadith cannot be proven sound, it is not disallowed to fast on a Saturday.
See: al-Talkhis al-Habir (2/216); Tahdhib as-Sunan (7/67); al-Furu‘ by Ibn Muflih (3/92); Majmu‘ Fatawa Ibn Baz (15/411); Fatawa al-Lajnah ad-Da’imah (10/396); Majmu‘ Fatawa Ibn ‘Uthaymin (20/35).
And Allah knows best.