All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The fasting of Prophet Daawood is the best way of fasting. He used to fast every other day, based on the authentic hadith narrated by Al-Bukhari and Muslim.
Whoever wants to combine the virtues of the fasting of Daawood as well as fasting on Mondays and Thursdays has obtained great goodness. It was narrated that the Prophet, sallallahu ‘alayhi wa sallam, said: “Deeds are displayed to Allah every Monday and Thursday, and I like that my deeds are shown while I am fasting.” [At-Tirmithi—Hasan Ghareeb—and An-Nasaa’i with a slight difference in wording]
Consequently, it is permissible to act in this way. Rather, it is considered a form of hastening to do good deeds. May Allah grant us all success to obey Him and spare us the evil of disobeying Him.
Allah Knows best.