‘Abdallah b. Busr, on the authority of his sister as-Samma’, reported God’s messenger as saying, “Do not fast on Saturday except during what has been made obligatory for you; and if one of you can get nothing but a grape skin or a piece of wood from a tree, he should chew it.”
Ahmad, Abu Dawud, Tirmidhi, Ibn Majah and Darimi transmitted it.
Abu Umama reported God’s messenger as saying, "If anyone fasts for a day while on jihad,* God will put between him and hell a ditch as wide as the distance between heaven and earth."
*Mirqat gives this meaning, but says it may refer to the hajj, the 'umra, seeking knowledge, or desiring to please God. The Arabic is 'in God’s way.'
Muslim al-Qurashi said that he or someone else asked God's messenger about perpetual fasting, and he replied, “You have a duty to your family. Fast during Ramadan and the following month, and every Wednesday and Thursday. You will then have observed a perpetual fast."