Was Jesus actually born in September?
"the theory that Jesus was born in September depends on the timing of John the Baptist’s birth. These biblical facts lay the groundwork: John’s father, a priest named Zechariah, was taking his turn to serve in the temple when the angel Gabriel appeared to him and announced that Elizabeth, Zechariah’s wife, would conceive a son (Luke 1:8–13). After Zechariah returned home, his wife conceived, just as the angel had said (Luke 1:23–24). Gabriel then visited Mary to announce the miraculous conception of Jesus, and this visit came in the sixth month of Elizabeth’s pregnancy (Luke 1:26, 36). Another important detail: Zechariah “belonged to the priestly division of Abijah” (Luke 1:5).
Using the above information, the calculations are made thus: the priests in the Abijah division served from June 13—19. Assuming that Elizabeth conceived shortly after Gabriel’s announcement to Zechariah, her sixth month—the month that Gabriel visits Mary—would be December or January. Assuming that Mary conceives shortly after Gabriel’s announcement to her,
Jesus would have been born nine months later, i.e., August or September."