The immediate context suggests that reference is made to the men listed in Acts 13:1.1 The Greek work translated as worshipping refers to official religious service done by church officers towards a body of believers.2 The concept of ministry/service work is a better translation of this word than public worship (see NASB (1995), NKJV and LEB). As a result, we should understand that the office bearers in Antioch were busy with service work in the church, and they spent time fasting/praying in order to reflect on God’s purpose for them and his church. New Testament fasting is typically associated with the prayerful reflection that is required when selecting office bearers (see Acts 14:23).3
2 While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.”