The Bible does not tell whether or not St. Augustine, St. John Chrysostom, or St. Francis of Assisi sometimes wrote under the inspiration of the Holy Spirit. Neither does the Bible tell us whether or not the books that we consider to be canonical really are. The Greek text of 2 Tim. 3:16 can be translated as,
16. All scripture is inspired by God and is useful for teaching, for reproof, for correction, and for training in righteousness, (NRSV)
16. Every scripture inspired by God is also useful for teaching, for reproof, for correction, and for training in righteousness, (NRSV, alternate translation found in a footnote)
16. Every writing inspired by God is also useful for teaching, for reproof, for correction, and for training in righteousness, (the Greek word rendered as Scripture is the common Greek noun for any written document)
If the rendering found in the text of the NRSV is the correct rendering, one must ask whether Paul was writing exclusively of the Old Testament canon, or the Old Testament canon plus some additional writing that he did not specify. If the rendering found in the NRSV footnote is the correct rendering, Paul may have been writing of an unspecified body of literature with which he and Timothy were familiar, but we are not. The Bible simply does not tell us what body of literature Paul is referring to.
If the third rendering is the correct rendering, Paul may have been writing of all inspired literature. The Bible simply does not tell us what literature Paul had in mind when he wrote 2 Tim. 3:16. In Jude vv. 14-15, Jude quotes from 1 Enoch, apparently believing it to be an inspired work. I personally believe that the Protestant canon is the final authority for doctrine and practice, but that is little more than my own personal belief. Are the deuterocanonical Books any less inspired than the books in the Protestant canon? The Bible does not answer that question, and the answer must be sought in a very careful study of these books. The very same things are true of the writing of the Ante-Nicene Church Fathers and the writings of others. It is also true, however, that many extracanonical writings have shaped to at least some extent what Baptists and other Christians believe today. All Christians, including Baptists, have their traditions that they tenacious cling to, but Baptists tend to be less willing to say so.