When was Jesus born in exactly?

In recent years, East Asian historians have attempted to match the birth of Jesus with special events in their history. They found that, according to the oldest record of the Comet Halley during the Han Dynasty, "The comet heads east with its tail pointing west at night, and was appearing in the sky for more than 70 days". in 6 BC. This has been suggested as an independent record of the "Star" described in Matthew 2. If accepted, this suggestion would place the birthday of Jesus in summer rather than winter.
Brief timeline of Jesus. Important years from empirical sources.
c. 6 BC – Suggested birth (Earliest)
c. 4 BC – Herod's death
c. AD 6 – Suggested birth (Latest). Quirinius census
c. AD 26 – Pilate appointed Judea governor
c. AD 27 – Suggested death (Earliest).
c. AD 36 – Suggested death (Latest);

SHOOT: The opening sentence says it all...The Gospels are problematic, because they offer two accounts that chronologists find incompatible.

clipped from www.thenazareneway.com The exact month or day or even the year of Jesus' birth cannot be exactly ascertained. Due to a mistaken calculation based on the Roman Calendar by Dionysius Exiguus in 525, it was long held that Jesus was born in the year 1 BC making the following year, AD 1, the first throughout which he was alive.  The Gospels are problematic, because they offer two accounts that chronologists find incompatible. Matthew states that Jesus was born while Herod the Great was still alive and that Herod ordered the slaughter of infants two years old and younger (Matt. 2:16), and based on the date of Herod's death in 4 BC (contra Dionysius Exiguus), many chronologists conclude that the year 6 BC is the most likely year of Jesus' birth. Consequently, Jesus would have been about four to six years old in the year AD 1.  On the other hand, Luke's account places Jesus' birth during a census conducted under the governorship of Quirinius, who, according to Josephus, conducted a census in AD 6.