Is it permissible to fast on Saturday along with Monday and Thursday with the intention of self-improvement, or is it absolutely forbidden to fast on Saturday?

Scholars have differed on the ruling of singling out Saturday for fasting, falling into two opinions:

The first opinion: The majority of scholars are of the view that it is disliked to single out Saturday for fasting, unless it coincides with a legitimate reason for fasting it, such as the Day of 'Arafah or 'Ashura, or if it aligns with a habitual fast, like one who fasts a day and breaks fast a day – this is permissible. They based their argument on the hadith of As-Sam'a' (may Allah be pleased with her) that the Prophet (peace be upon him) said: "Do not fast on Saturday except for what has been made obligatory upon you. If one of you finds nothing but grape skin or a tree branch, then let him chew it."

The second opinion: Some scholars are of the view that it is not disliked to fast on Saturday alone, absolutely; due to the lack of authenticity of what has been narrated regarding the prohibition of fasting it.

In summary: It is advisable not to single out Saturday for fasting. However, if it coincides with a fast one habitually observes, or a day that has a virtue in fasting, or if there is a need to fast it, such as it being a day when one is free from their busy affairs: then fasting it is not disliked.