The First Explicit Example of Transubstantiation in Church History

Q. When was the modern Roman dogma of transubstantiation first explicitly proposed?

A. Eight centuries after the death of Christ. 

Paschasius Radbertus, Abbot of Corbie (c. 785 - 865 A.D.):

Therefore, when He says: “This is My body” or My flesh, or: “This is My blood,” I do not think that He insinuated any other flesh than his own, which was born of the Virgin Mary, and hung upon the cross, nor any other blood than that which was shed upon the cross, and was then in His own body.

(J. P. Minge, Patrologiæ Cursus Completus, [1879], Patrologiæ Latinæ, Tomus CXX, S. Paschasii Radberti Abbatis Corbeiensis, Epistola Ad Frudegardum., Col. 1351). Here Trans. (J. H. Treat, The Catholic Faith; Or, Doctrines of the Church of Rome Contrary to Scripture and the Teaching of the Primitive Church, [1888], p. 239). Here

Let them, who will, dare extenuate this word of body, that that is not the true flesh of Christ, which is now celebrated in the Church of Christ, nor His true blood; wishing to approve of, or invent, I know not what, as if there were a certain virtue only of the flesh and blood in that Sacrament.  —Wherefore I wonder what certain will now say, that the truth of the flesh or blood of Christ is not in reality, but that in the Sacrament there is a certain virtue of the flesh, and not the flesh; there is a virtue of the blood, and not the blood; a figure, and not the truth: a shadow, and not the body. —I have said these things more at length, and more expressly for this reason, because I have heard that some blame me, as if in that book which I had published concerning the Sacraments of Christ, I intended to attribute to these words [This is Mybody] something more, or something else than the truth warrants.

(J. P. Minge, Patrologiæ Cursus Completus, [1879], Patrologiæ Latinæ, Tomus CXX, S. Paschasii Radberti Abbatis Corbeiensis, Expositum Paschasii Radberti, In Illud Matthæi, Matth. XXVI, Col. 1356, 1357). Here Trans. (J. H. Treat, The Catholic Faith; Or, Doctrines of the Church of Rome Contrary to Scripture and the Teaching of the Primitive Church, [1888], pp. 239-240). Here

Jesuit scholar, and canonized Roman saint, Cardinal Robert Bellarmine:

This author was the first, who seriously and profusely wrote concerning the truth of the body and blood of our Lord in the Eucharist, 

(De script. Eccl. de Paschas. Radbert., p . 276.) see (J. H. Treat, The Catholic Faith; Or, Doctrines of the Church of Rome Contrary to Scripture and the Teaching of the Primitive Church, [1888], p. 240). Here

~ Soli Deo Gloria