Final answer:
The Epistles of James and 1, 2, and 3 John were accepted into the canon over the course of the 4th century AD, with no specific year that marks their universal acceptance.
Step-by-step explanation:
The question pertains to the acceptance into the canon of the Epistles of James and 1, 2, and 3 John. These books of the New Testament were acknowledged as canonical by various Church councils and leaders over time. Though there isn't a universally agreed-upon year for when these texts were universally accepted into the canon, significant milestones include the Council of Laodicea (circa 363 AD), the Synod of Hippo (393 AD), and the Council of Carthage (397 AD), which all contributed to affirming the status of these texts as canonical. The process, however, was gradual and unfolded over centuries rather than a single date. Therefore, a precise year for their acceptance is not available, but they were largely recognized by the Christian communities and church leaders by the 4th century AD.