Tirmidhi

1:
The majority of scholars have interpreted this as a tanzihi prohibition, meaning that it is better not to fast.
The phrase "except for what Allah has made obligatory upon you" includes the obligatory fasts of vows (nadhar) and expiations (kaffarah).
Note:
(There is some discussion regarding its chain of narration;
see:
al-Irwa’ no. 960)

Benefits and Issues:
Saturday is the day of worship for the Jews, and we have been commanded to oppose them; therefore, if the days before or after are joined with it or included, there is no harm—for example, the white days (Ayyam al-Beedh), the days of Ashura, etc. However, if it is a make-up (qada) or vowed (nadhar) fast, or the Day of Arafah falls on a Saturday, or someone is practicing the fast of Dawud (sawm Dawud), then fasting on Saturday will be permissible.
Because this is not specification (takhsees).
By saying that this hadith is abrogated, Imam Abu Dawud perhaps, according to Allamah al-Albani rahimahullah, refers to the narration of Ibn Hibban and Hakim, in which Kuraib, the freed slave of Ibn Abbas radi Allahu anhu, says that Ibn Abbas and some other companions of the Messenger of Allah sallallahu alayhi wa sallam sent me to Umm al-Mu’minin Umm Salamah radi Allahu anha to ask her on which days the Messenger of Allah sallallahu alayhi wa sallam used to fast the most.
She replied that it was Saturday and Sunday.
I brought this answer to those gentlemen and informed them, and they (astonishingly) denied it.
Then all of them went to Umm al-Mu’minin and said: We had you asked such and such, and you gave such and such answer. She said: He has spoken the truth.
The Messenger of Allah sallallahu alayhi wa sallam used to fast most often on Saturdays and Sundays and used to say that these are the festival days of the polytheists, and I wish to oppose them.
Imam Hakim declared its chain to be authentic, and Dhahabi also agreed with him, but Allamah Abdul Haqq al-Ishbili rahimahullah declared its chain weak in al-Ahkam al-Wusta, and Allamah al-Albani rahimahullah also preferred this view.
(Irwa’ al-Ghalil, Hadith: 960) In short, the hadith is authentic and firm, not abrogated, and all objections are resolved by the very title of the chapter itself—that is, specifying this day alone is not permissible; it is necessary to join Friday or Sunday with it.

564 Lexical Explanation:
The “lam” in «لِحَاءَ عِنَبٍ» can be pronounced with either a fatha or a kasra, and there is a madd at the end. Its meaning is: peel. In «العنب», the “ayn” has a kasra beneath it and the “nun” has a fatha. The well-known fruit grape is called “inab” (grape).

«فَلْيَمُضَغْهَا» This chapter comes under both «نَصَرَا» and «فَتَحَ», meaning: that one may eat it and break the fast with it. Imam Tirmidhi rahimahullah has said that the prohibition of fasting on Saturday is because the Jews used to venerate Saturday. And this is also supported by the following hadith.

Narrator of the Hadith:
Hazrat Samā’ bint Busr radi Allahu anha, in «صماء» the “sad” has a fatha and the “mim” is mushaddad (doubled). Her «بُهَيَّه» was, and in «بهيه», the “ba” has a damma, the “ha” is open (with a fatha), and the “ya” is mushaddad (doubled). And according to one opinion, her name was «بُهَيْمَه» (with the addition of a “mim”). In “Busr,” the “ba” has a damma and the “ra” is sakin (silent). She belonged to the tribe of Mazin and was a female Companion (sahabiyyah). It has also been said about her that she was the sister of Abdullah bin Busr, and some have said paternal aunt, and some have said maternal aunt. ٭