I fast the white days (the thirteenth, the fourteenth and the fifteenth) every lunar month. At the same time, three days of fasting are due on me is as an oath expiation. Is it permissible to observe the fasts of the oath expiation during the white days? In other words, is it permissible to combine the two intentions?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If you fast the three days of the oath expiation on the white days which you usually fast, you are expected to receive the double rewards, i.e. you will be free from liability for the oath expiation and at the same time get the reward of fasting the white days. The juristic scholars state the validity of what is similar to this, e.g. if one observes a compensatory fast of Ramadan on the day of ‘Ashoora’, he is expected to get the double rewards, Allah willing. According to Shaykh Al-‘Uthaymeen :

The one who fasts the day of ‘Arafat or the day of ‘Ashoora’ while a compensatory fast of Ramadan is due on him, his fast is valid. Nevertheless, if he intends to fast on such a day for the compensation of Ramadan, he will receive the double rewards: the reward of the day of ‘Arafat/‘Ashoora’ along with the reward of the compensatory fast of Ramadan. That is so concerning the voluntary fast other than Ramadan.

According to Mughni Al-Muhtaj of Al-Khateeb Ash-Shirbeeni:

If someone said: the author of Al-Majmoo‘ said that the scholars of his juristic school left it without designation although designation is requisite for fasting the rawatib (confirmed voluntary fasts) such as ‘Arafat, ‘Ashoora’, the white days, and the six days of Shawwaal just like the regular Sunnah prayers, I say in reply that fasting on those days is principally assigned to them, in the sense that even if one intends to fast them with another intention (like making up for missed fasting in Ramadan or as expiation), he will receive the reward of fasting them too, the same as the prayer of tahiyyat al-masjid (mosque-greeting prayer), because what is meant is to fast on those days (regardless of the intention).

This text indicates that one receives the reward of fasting the white days even if he fasts them without the intention of the voluntary fast, since what is meant is to fast on those days (regardless of the intention). However, it is preferable to avoid making a double intention and rather intend the obligatory fast, and one will receive the reward of the voluntary fast too, Allah willing, even if he does not intend it. However, some scholars do not render making a double intention valid, as has been transmitted by As-Suyooti in Al-Ashbaah Wan-Nathaa’ir.

Allah knows best.