All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
We ask Allaah to grant you success and help you. You should know that voluntary fasting is of several ranks, and a slave of Allaah has to do his/her best as much as he/she can to ascend in ranks. Indeed, fasting has no equal (i.e. in reward and benefit) as stated in a Prophetic narration. The best fasting is that of Prophet Daawood (David) who would fast every other day, as stated in an authentic Prophetic narration.
At the very least, a Muslim should keep three fasts monthly. It was narrated on the authority of Abu Qataadah that the Prophet, sallallaahu ‘alayhi wa sallam, said: "[Fasting] three days every month and [the fasting of] Ramadan to Ramadan are [as good as] perpetual fasting." [Saheeh Muslim]
There is no doubt that fasting on Mondays and Thursdays is superior and that no other days could stand in their position, for the Prophet, sallallaahu ‘alayhi wa salam, favored them over other days by fasting on them. In justifying his fasting on them very often, he informed us that a person’s deeds are shown to Allaah The Almighty on these days, according to the narration by At-Tirmithi on the authority of Abu Qataadah ; and An-Nasaa'i on the authority of Usaamah .
Therefore, we advise you to do your best fast on them, and be sure that Allaah will make it easy for you to fast them, by His bounty. However, if you fast any other days, except for Friday solely or Saturday solely, then this would nonetheless be a good deed for which you would be rewarded.
Regardless of not having the same superiority as fasting on Monday and Thursday, fasting on any other day is included under the many Prophetic narrations that speak of the excellence of voluntary fasting. It would be sufficient to relate this Hadeeth narrated on the authority of Abu Umaamah that the Prophet, sallallaahu ‘alayhi wa salam, said: "Observe fasting, for it has no equal.” " [An-Nasaa'i]
Allaah Knows best.