Cyprian (c. 200-258) carried on a controversy with Stephen, the bishop of Rome, over how lapsed (but penitent) Christians were to be viewed and received by the Church. Their arguments deal with the basis for their stance, and Cyprian describes the stance of Stephen as the following: “Let nothing be innovated, says he, nothing maintained, except what has been handed down.” But Cyprian asks, “Whence is that tradition? Whether does it descend from the authority of the Lord and of the Gospel, or does it come from the commands and the epistles of the apostles? For that those things which are written down must be done, God witnesses and admonishes, saying to Joshua the son of Nun: ‘The book of this law shall not dpart out of they mouth; but thou shalt meditate in it day and night, that thou mayest observe to do according to all that is written therein.'” (Epistle 73:2)
During this same controversy, Firmilian, the Bishop of Caeserea wrote to Cyprian and explained his view that “they who are in Rome do not observe those things in all cases which are handed down from the beginning, and vainly pretend the authority of the apostles.” Here we see that it certainly was not the universal understanding that the bishop of Rome had some sort of special dispensation from Christ or Peter. Firmilian actually goes on to explain that Stephen the bishop of Rome is guilty of heresy and dividing the unity of the Church.
Again, my primary point being that clearly the early church fathers believed that the written Scriptures (“book of the law”) was the authoritative source of the teachings of Christ and the apostles.