St. Pope Leo the Great
Letter CLIX to Nicaetas, Bishop of Aquileia
VIII. About baptism by heretics.
For they who have received baptism from heretics, not having been previously baptized, are to be confirmed by imposition of hands with only the invocation of the Holy Ghost, because they have received the bare form of baptism without the power of sanctification. And this regulation, as you know; we require to be kept in all the churches, that the font once entered may not be defiled by repetition, as the Lord says, "One Lord, one faith, one baptism." And that washing may not be polluted by repetition, but, as we have said, only the sanctification of the Holy Ghost invoked, that what no one can receive from heretics may be obtained from catholic priests. This letter of ours, which we have sent in reply to the inquiries of the brotherhood you shall bring to the knowledge of all your brethren and fellow-bishops of the province, that our authority, now that it is given, may avail for the general observance. Dated 21st March, in the consulship of Majorian Augustus (458).
St. Fulgentius of Ruspe
The Rule of Faith, 43 [A.D. 524].
Anyone who receives the sacrament of baptism, whether in the Catholic Church or in a heretical or schismatic one, receives the whole sacrament; but salvation, which is the strength of the sacrament, he will not have, if he has had the sacrament outside the Catholic Church [and remains in deliberate schism]. He must therefore return to the Church, not so that he might receive again the sacrament of baptism, which no one dare repeat in any baptized person, but so that he may receive eternal life in Catholic society, for the obtaining of which no one is suited who, even with the sacrament of baptism, remains estranged from the Catholic Church
St. Pope Gregory the Great
Register of the Epistles of Saint Gregory the Great
Book VIII, Epistle LXVII
Gregory to Quiricus, Bishop, and the other catholic bishops in Hiberia
And indeed we have learnt from the ancient institution of the Fathers that whosoever among heretics are baptized in the name of the Trinity, when they return to holy Church, may be recalled to the bosom of mother Church either by unction of chrism, or by imposition of hands, or by profession of the faith only. Hence the West reconciles Arians to the holy Catholic Church by imposition of hands, but the East by the unction of holy chrism. But Monophysites and others are received by a true confession only, because holy baptism, which they have received among heretics, then acquires in them the power of cleansing, when either the former receive the Holy Spirit by imposition of hands, or the latter are united to the bowels of the holy and universal Church by reason of their confession of the true faith. Those heretics, however, who are not baptized in the name of the Trinity, such as the Bonosiaci and the Cataphyrae, because the former do not believe in Christ the Lord, and the latter with a perverse understanding believe a certain bad man, Montanus, to be the Holy Spirit, like unto whom are many others;--these, when they come to holy Church, are baptized, because what they received while in their error, not being in the name of the Holy Trinity, was not baptism. Nor can this be called an iteration of baptism, which, as has been said, had not been given in the name of the Trinity. But the Nestorians, since they are baptized in the name of the Holy Trinity-- though darkened by the error of their heresy in that, after the manner of Jewish unbelief, they believe not the Incarnation of the Only-begotten-- when they come to the Holy Catholic Church, are to be taught, by firm holding and profession of the true faith, to believe in one and the same Son of God and man, our Lord God Jesus Christ, the same existing in Divinity before the ages, and the same made man in the end of the ages, because The Word was made flesh and dwelt among us