The early Church admitted three valid methods of baptism: immersion, sprinkling, and pouring. But the Church admitted only one valid set of baptismal words, the Trinitarian. It wasn't enough to baptize only in the name of Jesus.
"After the foregoing instructions, baptize in the name of the Father, and of the Son, and of the Holy Spirit, in living [running] water. If you have no living water, then baptize in other water, and if you are not able in cold, then in warm. If you have neither, pour water three times on the head, in the name of the Father, and of the Son, and of the Holy Spirit. Before baptism, let the one baptizing and the one to be baptized fast, as also any others who are able. Command the one who is to be baptized to fast beforehand for one or two days" (Didache 7:1 [ca. A.D. 70]).
"When we are about to enter the water - no, just a little before - in the church and under the hand of the bishop, we solemnly profess that we renounce the devil and his pomps and his angels. Thereupon we are immersed three times" (The Crown 3:2 [A.D. 211]).
"At dawn a prayer shall be offered over the water. . . . Baptize first the children, and, if they can speak for themselves, let them do so. Otherwise let their parents or other relatives speak for them. Next baptize the men, and last of all the women. . . .
The presbyter then takes hold of each of those to be baptized and commands him to renounce, saying: 'I renounce you, Satan, and all your servants and all your works.' When he has renounced all these the presbyter shall anoint him with the oil of exorcism, saying: 'Let all spirits flee far away from you.' . . . Let them stand naked in the water. When the one being baptized goes down into the water, the one baptizing him shall put his hand on him and speak thus: 'Do you believe in God, the Father Almighty?' And he that is being baptized shall say: 'I believe.' Then, having his hand imposed upon the head of the one to be baptized, he shall baptize him once. Then he shall say: 'Do you believe in Christ Jesus . . . ?' And when he says: 'I believe,' he is baptized again. Again shall he say: 'Do you believe in the Holy Spirit and the holy Church and the resurrection of the flesh?' The one being baptized then says: 'I believe.' And so he is baptized a third time. Afterward, when he has come out, he is anointed with the consecrated oil, and the presbyter says, 'I anoint you with the holy oil in the name of Jesus Christ.' And so each one then dries himself, and immediately they put on their clothes. Then they come into the Church" (Apostolic Tradition 21 [ca. A.D. 215]).
"Why, when the Lord himself told his disciples that they should baptize all peoples in the name of the Father and of the Son and of the Holy Spirit, does this apostle employ the name of Christ alone in baptism, saying, 'We who have been baptized into Christ'; for indeed, legitimate baptism is had only in the name of the Trinity" (Commentary on Romans 5:8 [ca. A.D. 250]).
"The Church received from the apostles the tradition of giving baptism even to infants. The apostles, to whom were committed the secrets of divine mysteries, knew that there is in everyone the innate stain of sin, which must be washed away through water and the Spirit" (Ibid. 5:9).
"As [the heretic Novatian] seemed about to die, he received baptism in the bed where he lay, by pouring. . . . And when he recovered from his illness he did not receive the other things which, in accord with the law of the Church, it is necessary to have, nor was he sealed by the bishop" (Letter to Fabius of Antioch 6:43 [A.D. 251]).
"You have asked also, dearest son, what I thought about those who obtain the grace of God while they are weakened by illness - whether or not they are to be reckoned as legitimate Christians who have not been bathed with the saving water, but have had it poured over them. . . . I think that the divine benefits can in no way be weakened or mutilated, nor can anything less take place in that case, where that which is drawn from the divine gifts is accepted with full and entire faith both on the part of the giver and the receiver. . . . In the saving sacraments, when necessity compels and when God bestows his pardon, divine benefits are bestowed fully upon believers, nor ought anyone be disturbed because the sick are poured upon or sprinkled when they receive the Lord's grace" [Letter to a Certain Magnus 69(76):12 [A.D. 254]).
"He commanded them to baptize the Gentiles in the name of the Father and of the Son and of the Holy Spirit. How then do some say that though a Gentile be baptized . . . never mind how or of whom, so long as it be done in the name of Jesus Christ, the remission of sins can follow - when Christ himself commands the nations to be baptized in the full and united Trinity?" (Letter to Jubianus73:18 [A.D. 255]).
Cyril of Jerusalem
"You were led by the hand to the holy pool of divine baptism, as Christ was carried from the cross to this sepulcher here before us [in the Chapel of the Resurrection in Jerusalem]. And each of you was asked if he believed in the name of the Father, and of the Son, and of the Holy Spirit. And you confessed that saving confession, and descended three times into the water, and again ascended, and in this there was suggested by a symbol the three days of Christ's burial" [Catechetical Lectures 20:4 [ca. A.D. 350]).
Let no one be misled by the fact that the apostle [Paul] frequently omits the name of the Father and of the Holy Spirit when mentioning baptism, nor let anyone suppose that the invocation of the names is a matter of indifference. . . . The naming of Christ, you see, is the confession of the whole; it speaks the God who anoints, the Son who is anointed, and the Spirit who is the anointing. . . . If, then, in baptism the separation of the Spirit from the Father and the Son is perilous to the one baptizing and useless to the one receiving, how can it be safe for us to separate the Spirit from the Father and the Son? . . . So too then are we baptized in the name of the Father and of the Son and of the Holy Spirit" (The Holy Spirit 12:28 [A.D. 375]).