Question: My paternal grandmother observes Sawm (fast) three days a month plus every Monday and Thursday intending to do good deeds. However, she wasinformed that observing Sawm on these days is impermissible. We wish that Your Eminence will give us a fatwaa’ in this regard. May Allaah show mercy to you and reward you well!
Answer: Observing Sawm on Monday and Thursday is permissible. It is related by Aboo Daawood on the authority of Usaamah ibn Zayd (may Allaah be pleased with both of them) that the Prophet (peace be upon him) replied to the question of why he always observed Sawm on Monday and Thursday saying: The works of the people are presented (to Allaah) on Monday and Thursday. In another narration: I would like my deeds to be shown (to Allaah) while I am fasting. This Hadeeth clearly indicates that observing Sawm on Monday and Thursday is permissible and is a Sunnah (supererogatory act of worship following the example of the Prophet). Moreover, observing Sawm for three days of every month is also a Sunnah as stated in the Hadeeth authentically reported from the Prophet (peace be upon him)... read more here.