en_tn_condensed/act/18/17.md

they all seized

This may be an exaggeration to emphasize the strong feelings the people had. Alternate translation: "many people seized" or "many of them grabbed" (See: rc://en/ta/man/translate/figs-hyperbole)

So they all seized Sosthenes, the ruler of the synagogue, and beat him in front of the judgment seat

Possible meanings are 1) the Gentiles beat Sosthenes in the court in front of the judgment seat because he was the Jewish leader or 2) it is possible that Sosthenes was a believer in Christ, so the Jews beat him in front of the court.

Sosthenes, the ruler of the synagogue

"Sosthenes" was the Jewish ruler of the synagogue at Corinth. (See: rc://en/ta/man/translate/translate-names)

beat him

"repeatedly hit him" or "repeatedly punched him."