What is the ruling on fasting in the month of Shawwal?

It is recommended (mustahabb) to fast six days in the month of Shawwal after Ramadan. The Prophet (peace be upon him) said, “Whoever fasts the month of Ramadan and then follows it with six days from Shawwal, it is as if he has fasted for the whole year.” (Muslim, Sawm, 204 [1164]). These fasts can be observed consecutively or with intervals. (Ibn Abidin, Radd al-Muhtar, 2/435)

The voluntary fasts observed in Shawwal do not substitute for missed Ramadan fasts; that is, it is obligatory to make up the missed Ramadan fasts separately. Since it is not valid to intend both making up a missed fast and performing a voluntary fast with a single fast, one must intend only one of these when fasting in Shawwal. If one intends to make up missed Ramadan fasts while fasting in Shawwal, these fasts will count as make-up (qada) fasts.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu