From Abu Basir, from Abu Abdillah (peace be upon him), he said:
We performed Hajj with Abu Abdillah (peace be upon him) in the year in which his son Musa (peace be upon him) was born. When we stopped at al-Abwa', he set out lunch for us — and whenever he set out food for his companions he would make it abundant and good. He said: While we were eating, a messenger from Hamida came to him and said: "Hamida says to you: I have felt something different in myself, and I have felt what I used to feel when my delivery was near, and you had commanded me not to precede you with this son of mine." He said: So Abu Abdillah (peace be upon him) stood up and went with the messenger. When he left, his companions said to him: "May Allah bring you joy and may we be your ransom — what did Hamida do?" He said: "Allah has kept her safe and has gifted me a boy, and he is the best of what Allah has created among His creation'..." — the hadith continues.
Ref:
Al-Mahaasin, vol. 2, p. 314, H.no. 32
Al-Kafi, vol.1, p. 385, h.no. 1
Comment:
The narration reported in both Al-Mahaasin and Al-Kafi states that Imam al-Kadhim (peace be upon him) was born in al-Abwa’, between Mecca and Medina, during the year that Imam al-Sadiq (peace be upon him) performed Hajj.
While this narration confirms the location of the birth, it does not clearly establish whether it occurred before or after Hajj.
From Minhal al-Qassab, he said:
"I departed from Mecca intending Medina and I passed through al-Abwa' where Musa (peace be upon him) had just been born to Abu Abdillah (peace be upon him). I arrived in Medina before him and he entered after me by one day. He then fed the people for three days. I was among those who ate, and I would eat nothing until the next day when I would return and eat again. I continued like that for three days — eating until I was fully satisfied, then eating nothing until the next day."
Ref: Al-Mahaasin, vol.2, p. 418, H.no. 187
Comment:
Another narration from Minhal al-Qassab mentions passing through al-Abwa’ after leaving Mecca and finding that Imam al-Kadhim (peace be upon him) had just been born there.
This strongly indicates that the birth took place while Imam al-Sadiq (peace be upon him), his family, and companions were returning from Mecca to Medina after completing Hajj.
Although some later sources mention 7th Safar, these reports are not traced back to a source from Ahlul Bayt (peace be upon them).
In contrast, a narration in Dala’il al-Imamah, p.303, from Imam al-Askari (peace be upon him) explicitly states that Imam al-Kadhim (peace be upon him) was born in Dhul-Hijjah, 127 AH.
This is further supported by narrations encouraging pilgrims to leave Mecca soon after Hajj, making a much later date less likely.
Ref: al-Kafi, vol. 4, p. 521, H.no. 9
Based on the travel time from Mecca to al-Abwa’, the most likely dates are the 19th, 20th, or 21st of Dhul-Hijjah.
The 18th of Dhul-Hijjah (Eid al-Ghadir) appears less likely, as such a significant coincidence would probably have been mentioned explicitly in the narrations or become widely known.
The report that Imam al-Sadiq (peace be upon him) hosted three days of celebrations in Medina following the birth further supports that the birth took place in Dhul-Hijjah and before Moharram as it is not likely for Ahlul Bayt (peace be upon him) to celebrate in Moharram.
It is most likely that the celebration started on the 7th day of the birth as an Aqiqa, continued for three days, and ended before Moharram.
The available evidence points to the blessed birth of Imam al-Kadhim (peace be upon him) having occurred after Hajj and in the month of Dhul-Hijjah, most likely on the 19th, 20th, or 21st of Dhul-Hijjah. If one date is to be selected, the 20th of Dhul-Hijjah appears to be the most balanced estimate.
And Allah SWT knows best.