Analysis of information sources in references of the Wikipedia article "Believer's baptism" in English language version.
Walafrid Strabo recognized that the early Church only gradually extended baptism to newborns, that originally the sacrament was focused on adult converts
Likewise it seemed good that whosoever denies that infants newly from their mother's wombs should be baptized, or says that baptism is for remission of sins, but that they derive from Adam no original sin, which needs to be removed by the laver of regeneration, from whence the conclusion follows, that in them the form of baptism for the remission of sins, is to be understood as false and not true, let him be anathema. For no otherwise can be understood what the Apostle says, "By one man sin is come into the world, and death through sin, and so death passed upon all men in that all have sinned," than the Catholic Church everywhere diffused has always understood it. For on account of this rule of faith even infants, who could have committed as yet no sin themselves, therefore are truly baptized for the remission of sins, in order that what in them is the result of generation may be cleansed by regeneration.
When they baptize babies, pastors should make sure that their prayers include clear requests that God will bring the children to a personal faith that "owns" what the parents are promising at a time when the children (who "belong" from day one) cannot act for themselves. And when they dedicate children, pastors should make sure that their prayers include clear gratitude to God for the fact that he is already at work in the life of that child, who already "belongs" in the Christian community. Here's what must be stressed: whether at the time of baptism (in the adult baptism tradition) or at the time of confirmation when the vows made earlier by the parents are personally "owned" (in the infant baptism tradition), it is faith in Jesus (dependent trust, not mere cognitive affirmation) that is crucial. Paul goes so far as to say that without faith and obedience, the old rite of circumcision has no value (Romans 2:25). The same is true of baptism. With either rite, clear evangelistic follow-through is crucial.
the delay of baptism is preferable; principally, however, in the case of little children. For why is it necessary — if (baptism itself) is not so necessary — that the sponsors likewise should be thrust into danger? Who both themselves, by reason of mortality, may fail to fulfil their promises, and may be disappointed by the development of an evil disposition, in those for whom they stood? The Lord does indeed say, Forbid them not to come unto me. Let them come, then, while they are growing up; let them come while they are learning, while they are learning whither to come; let them become Christians when they have become able to know Christ.
7. When he had come to one of the cities not far away (the name of which is given by some ), and had consoled the brethren in other matters, he finally turned to the bishop that had been appointed, and seeing a youth of powerful physique, of pleasing appearance, and of ardent temperament, he said, 'This one I commit to you in all earnestness in the presence of the Church and with Christ as witness.' And when the bishop had accepted the charge and had promised all, he repeated the same injunction with an appeal to the same witnesses, and then departed for Ephesus. 8. But the presbyter taking home the youth committed to him, reared, kept, cherished, and finally baptized him. After this he relaxed his stricter care and watchfulness, with the idea that in putting upon him the seal of the Lord he had given him a perfect protection.
The Bogomils repudiated infant baptism, and considered the baptismal rite to be of a spiritual character neither by water nor by oil but by self-abnegation, prayers and chanting of hymns.