Albert Barnes Commentary Acts 19:15

"And the evil spirit answered and said unto them, Jesus I know, and Paul I know, but who are ye?" — Acts 19:15 (ASV)

Jesus I know. His power to cast out devils I know. (Compare to Matthew 8:29.)

Paul I know. Paul's power to cast out devils was also evident. (See Acts 19:12.)

But who are you? What power have you over evil spirits? By what right do you attempt to expel them? The meaning is, "You belong neither to Jesus nor Paul; you are not of their party; and you have no right or authority to attempt to work miracles in the name of either."