‘And God wrought special miracles by the hands of Paul, (in so much that to the sick were carried away from his body cloths or aprons), and the evil spirits went out.'
It was a period also of great signs and wonders, such that God wrought special miracles ‘through the hands of Paul' in an unprecedented way, probably literally. He laid hands on the sick and they recovered. He cast out evil spirits. On top of the wonders he himself performed, cloths (see Luke 19:20; John 11:44; John 20:7) and aprons were take from his body, and the suggestion would appear to be that these resulted in men and women being healed. But there is no need to see this as having been widespread. It is mentioned as unusual. The cloths may have been worn around his head as sweatbands, and the aprons have been worn while he was at work. Both may have been taken without his knowledge. This was no indication of a precedent to be followed.
The deliverance from evil spirits is probably a separate issue as they would be responsive to commands given in the name of Jesus (see following verses). Evil spirits are never cast out by the laying on of hands (and laying hands on a spirit possessed person is foolish for it encourages possession for the one who does it). They are cast out by the name of Jesus. But the whole point is that the wonders of the early days are being repeated (or are continuing), with Messianic healings and demonstrations of the defeat of the tyranny of Satan. This last was now to be highlighted by events that followed.