The word σάββατον occurs 68 times in the NT in a few forms. It has two distinct meanings (see BDAG)
- the seventh day of the week in Israel's calendar, marked by rest from work and by special religious ceremonies, sabbath
- (a) Singular, eg, Matt 12:2, 8, 24:20
- (b) Plural: meaning either: more than on sabbath, eg, Acts 17:2; or, meaning a single Sabbath, eg, Matt 12:1, 11, 28:1a, Mark 1:21, 2:23, 3:2, etc
- a period of seven days, week
- (a) Singular: Luke 18:12, Mark 16:2, 9, 1 Cor 16:2
- (b) Plural: "first day of the week" as in Matt 28:1b, Mark 16:2, Luke 24:1, John 20:1, 19, Acts 20:7, 1 Cor 16:2.
Note that the plural is often used for the singular but never the singular for the plural.
Note the comments of Professor Francois de Blois
The seventh day is designated by the Hebrew or Aramaic loan word
σάββατον (neuter singular) or σάββατα (neuter plural). Although there
are a few passages where σάββατα does in fact mean ‘two or more
Sabbaths’, in most cases both the singular and the plural forms are
used to designate a single Sabbath. In particular, in the Septuagint
we can observe that Hebrew šabbòṯ is translated either by σάββατον or
by σάββατα without any discernable difference of meaning. It seems
possible that σάββατα is in fact a borrowing of the Old Aramaic
singular noun in the determined state *šabbatā (Middle Aramaic:
šabbṯā), which Greek speakers subsequently reinterpreted as a neuter
plural and that the singular σάββατον is a back-formation.
Therefore, most versions translate the OP's quoted texts correctly, something similar to (my translation):
- Acts 13:14 - but they, having passed through from Perga, came to Antioch of Pisidia, and having gone into the synagogue of the day of the Sabbath, they sat down.
- Acts 16:13 - Then, on the day of the Sabbath, we went forth, outside the [city] gate, by a river, ...
In both cases, the word "day" is singular and thus, "sabbath" should be correctly translated in the singular.
In both cases, if using modern language, we might translate, Sabbath, as "Saturday" to use a modern English word, but this would not carry the correct meaning of "Sabbath", a rest day as Luke intended.
We can also observe several other features about the grammar of this word:
- the phrase, "τοῖς σάββασιν" (literally, "the Sabbaths") ALWAYS means "Sabbath in the singular, eg, Matt 12:1, 5, 10, 11, 12, Mark 1:21, 2:23, 24, 3:2, Luke 4:31, 6:2, 13:10.
- σάββατα (literally "Sabbaths") occurs only once in Acts 17:2 and means three successive Sabbaths.
- the phrase μίαν σαββάτων (literally "first of Sabbaths") simply means "the first day of the week", ie, "Sunday" in English, as in Matt 28:1, Mark 16:2, Luke 24:1, John 20:1, 19.
- the phrase τῶν σαββάτων (literally "the Sabbaths") always means "the Sabbath" (singular) as per, Luke 4:16, Acts 13:14, 16:13.