Is it permissible to combine the intention of making up for missed Ramadan fasts with the intention of observing a supererogatory fast (such as the fast of Ashura)?

This issue is known as the matter of combining or overlapping acts of worship. Whoever intends a supererogatory act will not be absolved from an obligatory one, like someone who intends to fast 'Ashura in lieu of making up for Ramadan. However, if one intends to make up for Ramadan and performs it on the day of 'Ashura, their makeup fast is valid, and it is hoped that they will attain the reward of 'Ashura according to some scholars.

Al-Ramli said: "And if one fasts in Shawwal for a makeup fast, or a vow, or other reasons, or on a day like 'Ashura, they will attain the reward of its supererogatory fasting."

Sheikh Ibn 'Uthaymeen said: "Whoever fasts on the Day of 'Arafah, or the Day of 'Ashura, and has makeup fasts from Ramadan due, their fast is valid. However, if they intend to fast this day as a makeup for Ramadan, they will receive both rewards: the reward of the Day of 'Arafah, and the reward of the Day of 'Ashura, along with the reward for the makeup fast."

One should hasten to make up for missed fasts. If time is short, then one should fast with the intention of making up, and perhaps they will attain the reward of 'Ashura or 'Arafah.