Did Jesus' disciples celebrate His birthday? Celebration of birthdays of some prominent persons was very much in vogue  at the time of Jesus, as we see at Mt 14:6. 

Now that Christmas has come to be one of the greatest feasts of Christianity, one wonders whether Jesus' birthday was celebrated even as He walked the earth. My question is: Do the apocryphal teachings of Catholic Church tell of of any occasion on which the birthday of Jesus was celebrated by the disciples ?
Did Jesus' disciples celebrate His birthday?

A valid question to say the least, but the short answer seems to be simply: no.

The Catholic Church has no such tradition from the Early Church or Church Fathers. The known Apocrypha are equally silent on this issue. 

The big problem with the Ancient Jews celebrating birthdays at the time of Christ is that the Jewish calendar was based on a lunar cycle and not a solar cycle like our present day calendar is based on. It is quite simple to understand this principle and the end result would be that Jesus’ actual birthday would vary from year to year according to the Jewish calendar.

The Disciples of Jesus were Jews and so was Jesus. They lived traditional Jewish lives and accepted Jesus as the Messiah. Their manner of worship changed after Jesus’ death. This question is asking about His birthday celebrations while Jesus was alive. 

Even Josephus admits that the Hebrew people did not celebrate birthdays.


  The first century Judahite historian Josephus noted that Judahite families did not celebrate birthdays:
  
  
    "Nay, indeed, the law does not permit us to make festivals at the birth of our children, and thereby afford occasion of drinking to excess" (Josephus. Translated by W. Whiston. Against Apion, Book II, Chapter 26. Extracted from Josephus Complete Works, Kregel Publications, Grand Rapids (MI), 14th printing, 1977, p. 632).
  
  
  There is no tradition in Judaism of celebrating birthdays, otherwise we would have a list of birthdays from Noah, Abraham to Moses, King David and many others, but no such thing exists. There are of course Sages who have suggested that certain individuals were born on Moedim or important days of Israel's history, however there are no "birthdays" within Judaism, Torah, Judahite Christians or the true Ecclesia of YEHOVAH God down through the ages.
  
  Now although there is no specific command against the celebration of birthdays in the Bible, the Judahite custom in those days was apparently based on the negative occurrences in the Bible surrounding birthdays, as well as the astrological implications of the celebration of birthdays (pagan practices, like astrology, were specifically prohibited in the law).
  
  Since nearly all of the first Christians were Judahites it's, this may partially explain why the celebration of the Messiah's birth would not be consistent with that early custom.
  
  In their essay titled "Birthdays, Jewishly," Lisa Farber Miller and Sandra Widener point out that the Encyclopedia Judaica is very blunt on this topic:
  
  
    "The celebration of birthdays is unknown in traditional Jewish ritual." 
  


For the rest of my response, I am going to let Rabbi Mendy Kaminker finish with the subject of birthdays according to the Ancient Hebrew nation.


  The First Birthday
  
  The first individual to celebrate a birthday was Adam. Well, considering that he wasn't "born," the stickler will argue that he didn't really have a "birthday"; but nonetheless, his first day on earth was quite eventful.
  
  Adam was created on the first Friday, the sixth day of creation, after G‑d finished setting the cosmic birthday table with the heavens and earth; sun and moon; plants and trees; beasts, fowl and fish. Shortly after Adam's creation, still on the same Friday, G‑d formed and breathed life into Eve.
  
  The results were considerably worse than a bad stomach acheThough there is no record of them partaking of a birthday cake, they celebrated by partaking of another delicacy—the fruit of the Tree of Knowledge. The results were considerably worse than a bad stomach ache.
  
  We celebrate the birthdays of Adam and Eve every year. Rosh Hashanah, the Jewish New Year, isn't observed on the day when the world was created, but six days later, on the anniversary of the creation of Adam and Eve. That is the day when everything truly began; the day when the Creator's vision of dwelling in a human-crafted home went into motion.
  
  An Intimidating Guest
  
  "And Abraham made a great feast on the day that Isaac was weaned" (Genesis 21:8).
  
  According to one opinion expressed in the Midrash, this feast celebrated Isaac's thirteenth birthday; the day when he was "weaned" from childhood and assumed the responsibilities of a Jewish adult. According to another opinion, this feast occurred on his second birthday. Either way, it was a birthday celebration.
  
  According to tradition, Isaac was born on Passover. As such, the "great feast" must have featured matzah and kosher for Passover cuisine. But the cuisine wasn't the main attraction—it was the distinguished guest list that included all the who's who of the time.
  
  One of the VIPs was Og, the king of Bashan, a gargantuan man with superhuman strength. He condescendingly commented: "Why is everyone fussing over this child? With my pinky I can end his life!"
  
  G‑d wasn't too pleased with this hubris. "Just wait. You will live to see hundreds of thousands of this boy's descendants. In fact, your end will be at their hands..."
  
  And that's precisely what happened—years later when he was vanquished by the Moses-led Israelite armies
  
  A "Memorable" Birthday Party
  
  The first scriptural reference to a birthday party is in the Book of Genesis. Pharaoh hosted a grand birthday party for all his ministers. During the course of the party he remembered two of his chamberlains, his chief butler and baker, whom he had incarcerated because of their negligence while on duty. Exactly as a Hebrew youth, Joseph, had foretold three days earlier, Pharaoh pardoned the butler and restored him to his post. The baker, on the other hand, was sent to the gallows.
  
  Until 120 Years Old... Really!
  
  A common Jewish birthday wish is, "May you live until 120." In the Torah we find a personality who lived until 120—on the nose. We're talking about Moses, the greatest prophet of all time, who was born and passed away on the same date—the 7th of Adar.
  
  Centuries later, when Haman wished to exterminate the Jews, he threw a lottery to determine the most propitious month to implement his nefarious plan. Haman was elated when the lottery chose the month of Adar, "this is the month when Moses, the Jews' savior, died!"
  
  But Haman didn't know that Adar is also the month when Moses was born. And the auspiciousness of a birthday offsets any negative qualities associated with death. The rest is history...
  
  A Mournful but Ultimately Joyous Birthday
  
  The redeemer was born the moment after the destructionThe saddest day on the Jewish calendar is the 9th of Av, the date when – among other tragedies – both holy temples were destroyed, leading to our nation's exile from the Holy Land. Nevertheless, our sages tell us that despite the sadness and pain, this is the birthday of Moshiach, our future redeemer:
  
  "On the day that the Holy Temple was destroyed, a Jew was plowing his field when his cow suddenly called out. An Arab was passing by and heard the low of the cow. Said the Arab: 'Jew, Jew! Unyoke your cow, free the stake of your plow, for your Holy Temple has now been destroyed.' The cow then lowed a second time. Said the Arab: 'Jew, Jew! Yoke your cow, reset the stake of your plow, for the Redeemer has now been born...'"
  
  The redeemer, and with him the potential for redemption, was born the moment after the destruction. - Birthdays in Jewish History


Whether Jesus celebrated his birthday or not is lost to history. Whether Mary or Joseph celebrated the Lord’s birthday is also lost to history. But the Church has resolved this issue with institution of the Feast of the Nativity of Our Lord Jesus Christ while placing this feast day on December 25th, now known as Christmas Day.


  But it was not till the fourth century that the Churches of the East began to keep the Feast of our Saviour’s Birth in the month of December. Up to that period they had kept it at one time on the sixth of January, thus uniting it, under the generic term of Epiphany, with the Manifestation of our Saviour made to the Magi, and in them to the Gentiles; at another time, as Clement of Alexandria tells us, they kept it on the 25th of the month Pachon (May 15), or on the 25th of the month Pharmuth (April 20). St John Chrysostom, in the Homily we have just cited, which he gave in 386, tells us that the Roman custom of celebrating the Birth of our Saviour on December 25 had then only been observed ten years in the Church of Antioch. It is probable that this change had been introduced in obedience to the wishes of the Apostolic See, wishes which received additional weight by the edict of the Emperors Theodosius and Valentinian, which appeared towards the close of the fourth century, and decreed that the Nativity and Epiphany of our Lord should be made two distinct Festivals. The only Church that has maintained the custom of celebrating the two mysteries on January 6 is that of Armenia; owing, no doubt, to the circumstance of that country not being under the authority of the Emperors; as also because it was withdrawn at an early period from the influence of Rome by schism and heresy. - The History of Christmas (Dom Guéranger)