Is it permissible to fast one day and break the fast the next with the intention that the fasting is a Sunnah for the sake of Allah?

If you wish to fast one day and break your fast the next as a voluntary act for the sake of Allah, this is the best form of fasting, as stated in the Prophet's (peace be upon him) hadith (definition) to Abdullah ibn Amr ibn al-Aas: "Fast one day and break your fast the next; that is the fasting of David (peace be upon him), and it is the best of fasting." If a person who is voluntarily fasting intentionally breaks their fast, there is no sin upon them, because a volunteer is their own master. The acceptance of the fast rests with Allah the Almighty, and it is incumbent upon the Muslim to be sincere in intention, follow the Sunnah (definition), and have a good opinion of Allah.