Answered by Shaykh Amjad Rasheed
What is the fast of our master Dawud? Which is the best day to start this fast?
The fast of our master Dawud is to fasting every other day. This is the best of fasts, as is confirmed in the authentic hadith, related by Bukhari and Muslim.
If one happens to begin this fast on a day that is offensive (makruh) to single out for fasting, such as Friday, then it is sunna to fast on that day only for the one who is performing the fast of our master Dawud. This is not offensive in and of itself according the Ibn Qasim, in Hashiya al-Tuhfa (459/3).
There is no specific day that is preferred to begin the fast of Dawud; any day that one chooses to begin his fast and remain constant on it will obtain the reward.