Is a make-up fast (for a woman) considered "fasting in the path of Allah" as stated in the noble Hadith: "Whoever fasts one day in the path of Allah, Allah will distance him from Hellfire the distance of a hundred years"?

The wording of the hadith mentioned, "Whoever fasts a day in the way of Allah," is not the one found in the books of Sunnah. The established wording is what Abu Sa'id Al-Khudri narrated from the Prophet, peace and blessings be upon him: "Whoever fasts a day in the way of Allah, Allah will distance his face from the Hellfire for seventy autumns."

Scholars have differed regarding the meaning of "in the way of Allah." Some believe it means sincerity of intention towards Allah the Almighty, while others believe it means fasting while engaged in jihad in the way of Allah, which is the more readily apparent meaning. Accordingly, making up missed Ramadan fasts with sincerity towards Allah the Almighty falls under this hadith, based on the interpretation of "in the way of Allah" as sincerity of intention.