Acts of the Holy Apostle and Evangelist John the Theologian - Apocryphal. Some of the Fathers ascribe authorship to the heretic Leucius. From the Ante-Nicene Fathers, vol. 8, American edition. In HTML, with notes, at Christian Classics Ethereal Library.
The Beloved Disciple - Long hagiography of St. John, by Howard Cannon, contains a lot of legendary material.
Greek Orthodox Archdiocese of Australia - The Synaxis of St. John the Baptist and Forerunner of Christ, celebrated in the Christian East on 7 January, the day after Epiphany, in commemoration of the translation of his relic (hand) to Constantinople.
For All the Saints - Entry for the feast of the Birth of John the Baptist has little about his birth but more about his life.
Greek Orthodox Archdiocese of Australia - The Nativity of the Honourable Forerunner, St. John the Baptist. John is unusual in that he is the only saint, besides the Blessed Virgin Mary, whose birth we celebrate liturgically.