The sacrament of confirmation is found in Acts 8:14-17: "The two (Peter and John) went down to these people and prayed that they might receive the Holy Spirit. It had not as yet come down upon any of them since they had only been baptized in the name of the Lord Jesus. The pair upon arriving imposed hands on them and they received the Holy Spirit".
In Hebrews 6:2 we read: "Therefore let us leave the elementary teachings of Christ and go on to maturity, not laying again the foundation of repentance from acts that lead to death, and of faith in God, instruction about baptisms, the laying on of hands, the resurrection of the dead, and eternal judgment." This passage shows that confirmation is an important step in the Christian journey–along with repentance, faith, baptism, resurrection, and judgment. This is the order of Christian salvation.
The laying on of hands in this passage must mean confirmation. Elsewhere, laying on of hands refers to priestly ordination, but in Hebrews, laying on of hands refers to something done universally, to each Christian.
The Church Fathers also recognized confirmation, even though the sacrament was given right along with baptism.
Tertullian (The Resurrection of the Dead 8:2 [A.D. 210]) "No soul whatever is able to obtain salvation unless it has believed while it was in the flesh. Indeed, the flesh is the hinge of salvation . . . The flesh, then, is washed [baptism] so that the soul may be made clean. The flesh is anointed so that the soul may be dedicated to holiness. The flesh is signed so that the soul may be fortified. The flesh is shaded by the imposition of hands [confirmation] so that the soul may be illuminated by the Spirit. The flesh feeds on the body and blood of Christ [the Eucharist] so that the soul too may feed on God. They cannot, then, be separated in their reward, when they are united in their works".
Hippolytus (The Apostolic Tradition, 21 [A.D. 215]) "The bishop, imposing his hand on them, shall make an invocation, saying, 'O Lord God, who made them worthy of the remission of sins through the Holy Spirit's washing unto rebirth, send into them your grace so that they may serve you according to your will, for there is glory to you, to the Father and the Son with the Holy Spirit, in the holy Church, both now and through the ages of ages. Amen.' Then, pouring the consecrated oil into his hand and imposing it on the head of the baptized, he shall say, 'I anoint you with holy oil in the Lord, the Father Almighty, and Christ Jesus and the Holy Spirit.' Signing them on the forehead, he shall kiss them and say, 'The Lord be with you.' He that has been signed shall say, 'And with your spirit.' Thus shall he do to each".
Cyprian of Carthage (Letters 73:9[A.D. 253]) "Some say in regard to those who were baptized in Samaria that when the apostles Peter and John came there only hands were imposed on them so that they might receive the Holy Spirit, and that they were not re-baptized. But we see, dearest brother, that this situation in no way pertains to the present case. Those in Samaria who had believed had believed in the true faith, and it was by the deacon Philip, whom those same apostles had sent there, that they had been baptized inside--in the Church. . . . Since, then, they had already received a legitimate and ecclesiastical baptism, it was not necessary to baptize them again. Rather, that only which was lacking was done by Peter and John. The prayer having been made over them and hands having been imposed upon them, the Holy Spirit was invoked and was poured out upon them. This is even now the practice among us, so that those who are baptized in the Church then are brought to the prelates of the Church; through our prayer and the imposition of hands, they receive the Holy Spirit and are perfected with the seal of the Lord"
Treatise on Re-Baptism (Treatise on Re-Baptism 1 [A.D. 256]) "By imposition of the bishop's hands the Holy Spirit is given to every one that believes, as in the case of the Samaritans, after Philip's baptism, the apostles did to them by laying on of hands [Acts 8:14].
Serapion (The Sacramentary of Serapion, 25:1 [A.D. 350]) "'God of powers, aid of every soul that turns to you and comes under your powerful hand in your only-begotten. We beseech you, that through your divine and invisible power of our Lord and Savior Jesus Christ, you may effect in this chrism a divine and heavenly operation, so that those baptized and anointed in the tracing with it of the sign of the saving cross of the only-begotten . . . as if reborn and renewed through the bath of regeneration, may be made participants in the gift of the Holy Spirit and, confirmed by this seal, may remain firm and immovable, unharmed and inviolate'".
Cyril of Jerusalem (Catechetical Lectures, 21:1, 3 [A. D. 350])"After you had come up from the pool of the sacred streams, there was given chrism, the antitype of that with which Christ was anointed, and this is the Holy Spirit. But beware of supposing that this is ordinary ointment. For just as the bread of the Eucharist after the invocation of the Holy Spirit is simple bread no longer, but the body of Christ, so also this ointment is no longer plain ointment, nor, so to speak, common, after the invocation. Further, it is the gracious gift of Christ, and it is made fit for the imparting of his Godhead by the coming of the Holy Spirit. This ointment is symbolically applied to your forehead and to your other senses; while your body is anointed with the visible ointment, your soul is sanctified by the holy and life-giving Spirit. Just as Christ, after his baptism, and the coming upon him of the Holy Spirit, went forth and defeated the adversary, so also with you after holy baptism and the mystical chrism, having put on the panoply of the Holy Spirit, you are to withstand the power of the adversary and defeat him, saying, 'I am able to do all things in Christ, who strengthens me'".
Pacian of Barcelona (Three Letters to the Novatianist Sympronian, 1:6 [A.D. 33 ])"If, then, the power of both baptism and confirmation, greater by far than charisms, is passed on to the bishops, so too is the right of binding and loosing".