Fiqh-us-Sunnah Volume 3, Zakaat and Fasting, Fiqh 3.122.

Busr as-Salmi related from his sister as-Sama’ that the Messenger of Allah, upon whom be peace, said: “Do not fast on Saturdays unless it is an obligatory fast. [You should not fast] even if you do not find anything [to eat] save some grape peelings or a branch of a tree to chew on.”

This is related by Ahmad, an-Nasa’i, at-Tirmizhi, Abu Dawud, Ibn Majah, and al-Hakim. Al-Hakim said that it is sahih according to the conditions of Muslim, while at-Tirmizhi called it hassan. AtTirmizhi said that what is disliked here is for a person to exclusively choose Saturday as a day of fasting, as it is the day that the Jews honour.

In contradiction with the preceding report, Umm Salamah claims: “The Prophet used to fast more often on Saturdays and Sundays than on the other days. He would say: ‘They are the ‘ids of the polytheists, and I love to differ from them.'” This is related by Ahmad, al-Baihaqi, al-Hakim, and Ibn Khuzaimah who called it sahih.

The Hanafiyyah, Shaf’iyyah, and Hanbaliyyah say it is disliked to fast on Saturday by itself due to the preceding evidence. Malik differs from them, but the hadith is proof against him.