Albert Barnes on John 10:25

I told you. It is not recorded that Jesus had told them in so many words that he was the Christ, but he had used expressions designed to convey the same truth, and which many of them understood as claiming to be the Messiah. See Jn 5:19, 8:36,56, 10:1. The expression "the Son of God" they understood to be equivalent to the Messiah. This he had often used of himself in a sense not to be mistaken.

The works. The miracles, such as restoring the blind, curing the sick, &c.

In my Father's name. By the power and command of God. Jesus was either the Messiah or an impostor. The Pharisees charged him with being the latter (Mt 26:60,61, 27:63, Jn 4:36); but God would not give such power to an impostor. The power of working miracles is an attestation of God to what is taught. Mt 4:24.

(y) "the works that I do" Jn 5:36