Historically, what are the earliest writings that indicate controversy or differing opinions regarding the interpretation of the anarthrous θεός in John 1:1? This debate continues today between those who advocate the translation "the Word was God" against those who prefer "the Word was a god."
The earliest mention of controversy appears to be in the writings of Origen of Alexandria, in the third century. He indicates that some debate already existed on the matter in his time, and he attempts to resolve it by saying that the lack of the article implies that the Word of God is inferior to and dependent on the "True God":
We next notice John’s use of the article in these sentences. He does not write without care in this respect, nor is he unfamiliar with the niceties of the Greek tongue. In some cases he uses the article, and in some he omits it. He adds the article to the Logos, but to the name of God he adds it sometimes only. He uses the article, when the name of God refers to the uncreated cause of all things, and omits it when the Logos is named God. [...]
Now there are many who are sincerely concerned about religion, and who fall here into great perplexity. They are afraid that they may be proclaiming two Gods, and their fear drives them into doctrines which are false and wicked. Either they deny that the Son has a distinct nature of His own besides that of the Father, and make Him whom they call the Son to be God all but the name, or they deny the divinity of the Son, giving Him a separate existence of His own, and making His sphere of essence fall outside that of the Father, so that they are separable from each other.
To such persons we have to say that God on the one hand is Very God (Autotheos, God of Himself); and so the Saviour says in His prayer to the Father, “That they may know Thee the only true God;” but that all beyond the Very God is made God by participation in His divinity, and is not to be called simply God (with the article), but rather God (without article). And thus the first-born of all creation, who is the first to be with God, and to attract to Himself divinity, is a being of more exalted rank than the other gods beside Him, of whom God is the God, as it is written, “The God of gods, the Lord, hath spoken and called the earth.” [...]
The true God, then, is “The God,” and those who are formed after Him are gods, images, as it were, of Him the prototype. But the archetypal image, again, of all these images is the Word of God, who was in the beginning, and who by being with God is at all times God, not possessing that of Himself, but by His being with the Father, and not continuing to be God, if we should think of this, except by remaining always in uninterrupted contemplation of the depths of the Father. (Commentary on the Gospel of John, 2.2; paragraph breaks and bold added)
A century later, John Chrysostom argued the opposite side, noting other biblical texts supporting the full divinity of Christ, and remarking on the grammatical issue:
“Yet observe,” says he, “the Father is named with the addition of the article, but the Son without it.” What then, when the Apostle says, “The Great God, and our Saviour Jesus Christ” (Tit. ii. 13); and again, “Who is above all, God”? (Rom. ix. 5.) It is true that here he has mentioned the Son, without the article; but he does the same with the Father also, at least in his Epistle to the Philippians (c. ii. 6), he says, “Who being in the form of God, thought it not robbery to be equal with God”; and again to the Romans, “Grace to you, and peace, from God our Father, and the Lord Jesus Christ.” (Rom. i. 7.)
Besides, it was superfluous for it to be attached in that place, when close above it was continually attached to “the Word.” For as in speaking concerning the Father, he says, “God is a Spirit” (John iv. 24), and we do not, because the article is not joined to “Spirit,” yet deny the Spiritual Nature of God; so here, although the article is not annexed to the Son, the Son is not on that account a less God. Why so? Because in saying “God,” and again “God,” he does not reveal to us any difference in this Godhead, but the contrary; for having before said, “and the Word was God”; that no one might suppose the Godhead of the Son to be inferior, he immediately adds the characteristics of genuine Godhead, including Eternity, (for “He was,” says he, “in the beginning with God,”) and attributing to Him the office of Creator. (Homilies on the Gospel of John, 4)