When a fast day (other than Yom Kippur) falls on Shabbat, when fasting is prohibited, the fast is observed the following day, on Sunday. Thus, for example, in a year when Rosh Hashanah falls on Thursday and Friday, in which case the fast of Som Gedalya falls on Shabbat, we observe the fast on Sunday. This applies as well to the fasts of Asara Be’Tebet, Shiba Asar Be’Tamuz and Tisha B’Ab.
In such a case, when a fast is delayed until the next day, certain individuals are exempt from the fast. For example, a bride and groom within the seven days of their wedding are not required to fast on a Ta’anit Dehuya (deferred fast day). Similarly, if a Berit Mila takes place on a Ta’anit Dehuya, then the infant’s father, the Sandak (person who holds the infant during the Berit) and the Mohel (one who performs the Berit) do not fast on that day.
A number of works (Elya Rabba 549:6, Shaareh Teshuba 549:1) cite the view of the Rosh Yosef that this exemption applies every year in Som Gedalya, regardless of on which day it falls. This view follows the tradition that Gedalya Ben Ahikam, whose tragic murder we commemorate by fasting on Som Gedalya, was assassinated on Rosh Hashanah itself. It is only because Halacha does not allow fasting on the holiday of Rosh Hashanah that we delay the fast until the day after Rosh Hashanah. In essence, then, the fast of Som Gedalya is always a Ta’anit Dehuya; it is "deferred" ever year until after Rosh Hashanah. Hence, according to the Rosh Yosef, the people mentioned above – brides, grooms, and people involved in a Berit Mila – are not required to fast any year on Som Gedalya.
However, Halacha does not follow this view of the Rosh Yosef. We accept the tradition that Gedalya’s assassination in fact took place on the third of Tishri, after Rosh Hashanah, on the day we observe as Som Gedalya. This is indeed the implication of the Gemara in Masechet Rosh Hashanah (17), and this appears also in the Sha’ar Hakavanot and Kaf Ha’haim. Therefore, in a year when Som Gedalya does not fall on Sunday, everyone must fast, including the people listed above. This is the ruling of Hacham Ben Sion Abba Shaul, in his work Or Le’sion (vol. 3, 29:9). It is only when Som Gedalya falls on Shabbat and is then deferred to Sunday that these people are exempt from the fast, as is the case regarding the other fast days.
Summary: When Som Gedalya, Shiba Asar Be’Tamuz, Tisha B’Ab or Asara Be’Tebet falls on Shabbat, the fast is deferred to Sunday. In such a case, the following people are exempt from the fast: a bride and groom within seven days of their wedding, a Mohel who performs a Berit Mila that day, a Sandak who holds a baby during a Berit that day, and a father who makes a Berit Mila for his son that day.
