Here is the information that I have found on this
In which year was Jesus born?
History records that Herod the Great died (Mt. 2:19) in 4 BC, so, if Jesus was born within Herod’s reign, as Matthew states (Mt. 2:1), then He must have been born before 4 BC.
The Star of Bethlehem (Beit Lechem in Hebrew) (Mt. 2:2) may have been a comet, or a planetary conjunction between Venus and Jupiter on March 11th in 5 BC, or another conjunction between Venus and the crescent of the 3-day old New Moon on April 10th 5 BC (which would have combined to look like a comet's tail), but modern astronomers' best guess is that it was a nova (a star undergoing a temporary outburst of radiation) in the constellation of Aquila, also in 5 BC – it is now only a 16th-magnitude star. We don't really know which of these was the Star of Bethlehem, but we can be pretty sure the year was 5 BC!
Some people think that this shows that Jesus must have been born in the Spring of 5 BC, but they are ignoring the fact that, if Herod wanted to kill all boys under the age of two (Mt. 2:16), it was probably because Jesus was about one year old at the time. Thus, Jesus was probably born in the previous year – 6 BC.
Luke tells that a census was ordered by Augustus (Lk. 2:1) and carried out by Quirinius (or Cyrenius), the governor of Syria (Lk. 2:2). Now, Quirinius was "legat" of Syria in 6 AD, but many bible historians hold the opinion that he was also in office (as a consul) 13 years earlier (i.e. in 8 BC), and newer research has found that there was a census ordered by Rome in 12 BC, which was not concluded until after 7 BC (orders took time, and Syria was on the edge of the Roman Empire!) Thus, if Jesus was born in 6 BC, it is still possible that Luke’s account is historically accurate.
At what time of year was Jesus born?
Lk. 2:1 tells us that at this time Caesar Augustus had decreed that all the world should be taxed. We may be assured that Quirinius would not have ordered a census to be taken in winter, at the worst possible period for travel; but Luke's account that the shepherds were abiding in the field keeping watch over their flocks by night (Lk. 2:8) lets us know that Jesus was born in summer or early autumn. Since December is cold and rainy in Judea, it is likely the shepherds would have sought shelter for their flocks at night.
If we are going to narrow down the date of Jesus's birth any further, it is going to be necessary to understand how the Hebrew calendar worked.