Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh

Fasting the month of Ramadan is the fourth pillar of Islam enjoined upon every Muslim. Only individuals in particular categories are allowed to skip the fast. Those excused include persons with health, traveling, or elderly who cannot endure the pangs of hunger and thirst, and in case of women (those menstruating or undergoing postnatal period of bleeding, or women who are pregnant or breastfeeding).

The case of Kaffarah for a broken oath is different; if you have broken a sworn oath, you are obligated  to expiate for the offense, and it must be done outside the month of Ramadan; the obligatory fasting of Ramadan cannot count towards that; as such, it cannot absolve you of your duty of this duty.

However, it is possible to do so while fasting the six days of Shawwal as some scholars including those of the Shafi school have ruled: they allow for a double intention in case of voluntary fasts.

I pray to Allah to grant us steadfastness in the practice of Islam.

Almighty Allah knows best.