Bukhari

Hadith Commentary:
In Al-Hakim and others, it is narrated marfu‘an from Abu Hurairah (radi Allahu anhu):
«يَوْمُ الْجُمُعَةِ عِيدٌ فَلَا تَجْعَلُوا يَوْمَ عِيدِكُمْ يَوْمَ صِيَامِكُمْ إِلَّا أَنْ تَصُومُوا قَبْلَهُ أَوْ بَعْدَهُ» That is, the day of Jumu‘ah is a day of Eid for you, so do not make your Eid day a day of fasting, except that you fast a day before or after it.

Ibn Abi Shaybah has transmitted from Ali (radi Allahu anhu) that one should not fast on the day of Jumu‘ah; this day is for you a day of worship of Allah and eating and drinking.

And the majority (jumhur) are of the view that the prohibition is for discouragement (tanzih) (Fath).
That is, the opinion of the majority is that the prohibition of fasting on the day of Jumu‘ah is for discouragement, not for prohibition (hurmah), meaning it is better not to fast.

Hadith Commentary:
(1)
It is narrated from Imam Malik, he says:
I have not heard anyone prohibiting fasting on Friday; fasting on Friday is good.
If Imam Malik had received the aforementioned hadith, he would not have opposed it.
In any case, fasting on Friday individually is prohibited.
Its wisdom is explained as follows: Friday is a day of supplication, remembrance, and worship.
On this day, ritual bath (ghusl) and other acts are performed, and the sermon is listened to; therefore, breaking the fast helps in performing these acts and makes them easier to carry out. Furthermore, fasting only on Friday may lead to exaggeration in its veneration, because the Jews used to fast only on the day they gathered in their places of worship, and we have been commanded to oppose them.
It is mentioned in the hadith:
Do not single out Friday among other days for fasting unless it coincides with a day on which one is already fasting.
(Sahih Muslim, Kitab al-Siyam, Hadith: 2684(1144))
Some people say:
The reason for prohibiting singling out Friday for fasting is that Friday has been called an Eid, as mentioned in the hadith:
“Friday is your day of Eid.”
(Musnad Ahmad: 532/2)
And it is unanimously prohibited to fast on the day of Eid; however, the difference between Friday and Eid is that fasting is prohibited on Eid in all circumstances, whereas on Friday, fasting becomes permissible if one fasts a day before or a day after as well.
In this regard, Imam Bukhari rahimahullah has presented three ahadith.
There is some brevity in the first two ahadith, but the third hadith contains complete detail, from which it is understood that if one wishes to fast on Friday, then one should also fast a day before or a day after.
There is further detail regarding this in Sahih Muslim; the Messenger of Allah sallallahu alayhi wa sallam said:
“Do not single out the night of Friday for worship or its day for fasting unless it is a fast that one observes regularly.”
(Sahih Muslim, Kitab al-Siyam, Hadith: 2684(1144))
(2)
Hafiz Ibn Hajar rahimahullah writes:
If the fast of Arafah falls on a Friday, or it is a fast of vow (nadhar), for example: a vow for the recovery of a sick person or the return of a lost one, and it happens to fall on a Friday, then fasting on that day is permissible.
(Fath al-Bari: 297/4)

Benefits and Issues:
It is permissible to fast on Saturday, but one should combine it with either the preceding or following day.
Similarly, this has already been mentioned regarding Friday.