What question did the religious leaders ask Peter after the healing in Acts 4?
After the healing, the religious leaders asked Peter by what power or by what name he had done this. They demanded the source of his authority and the name invoked in the miracle on the layman. This remained the point of controversy.
Les explains that after Peter and the others were arrested and put in hold until the next day, the rulers, elders, and scribes gathered in Jerusalem with Annas the high priest, Caiaphas, John, and Alexander. When Peter and the others were set in their midst, they asked, 'By what power, or by what name, have you done this?' Les points out this was the point of controversy over the miracle performed on a layman. He also notes these rulers were Israel's religious leaders, the priests, and that Peter, filled with the Holy Spirit, began to answer them.
And when they had set them in the midst, they asked, By what power, or by what name, have ye done this?