A.T. Robertson Commentary Acts 13:43

"Now when the synagogue broke up, many of the Jews and of the devout proselytes followed Paul and Barnabas; who, speaking to them, urged them to continue in the grace of God." — Acts 13:43 (ASV)

When the synagogue broke up (λυθεισης της συναγωγης). Genitive absolute of first aorist passive participle of λυω. Apparently Paul and Barnabas had gone out before the synagogue was formally dismissed.

Of the devout proselytes (των σεβομενων προσηλυτων). Of the worshipping proselytes described in verses 16,25 as "those who fear God" (cf. 16:14) employed usually of the uncircumcised Gentiles who yet attended the synagogue worship, but the word προσηλυτο (προσ, ηλυτος verbal from ερχομα, a new-comer) means usually those who had become circumcised (proselytes of righteousness). Yet the rabbis used it also of proselytes of the gate who had not yet become circumcised, probably the idea here. In the N.T. the word occurs only in Mt 23:15; Acts 2:10; 6:5; 13:43. Many (both Jews and proselytes) followed (ηκολουθησαν, ingressive aorist active indicative of ακολουθεω) Paul and Barnabas to hear more without waiting till the next Sabbath. So we are to picture Paul and Barnabas speaking (προσλαλουντες, late compound, in N.T. only here and 28:20) to eager groups.

Urged (επειθον). Imperfect active of πειθω, either descriptive (were persuading) or conative (were trying to persuade). Paul had great powers of persuasion (18:4; 19:8,26; 26:28; 28:23; 2 Corinthians 5:11; Galatians 1:10). These Jews "were beginning to understand for the first time the true meaning of their national history" (Furneaux), "the grace of God" to them.