Jamieson, Fausset and Brown on Acts 13:42-43

42-43. And when the Jews were gone out of the synagogue, the Gentiles besought that these words might be preached to them the next sabbath--rather (according to what is beyond doubt the true reading), "Now, as they were going out [of the synagogue], they besought"--that is, not the Gentiles, whose case comes in afterwards, but the mixed congregation of Jews and proselytes, to whom the discourse had been addressed, entreated to have another hearing of such truths; those of them, that is, who had been impressed. "And after the breaking up of the synagogue, many of" both classes, Jews and religious; proselytes, followed Paul and Barnabas (observe, from this time forward, the inverted order of these names; except Ac 14:14; 13:7; 12:25; see on Ac 14:14; Ac 13:7; Ac 12:25). These names evidently been won to the Gospel by what they had heard, and felt a clinging to their spiritual benefactors.