Prophet Muhammad (PBUH) had three sons and four daughters. All of his children were born to Hz Khadijah bint Khuwaylid (RA) except one son (Ibrahim), who was born to Hz Maria al-Qibtiyah (RA).
In the order of birth sequence, the children of Prophet Muhammad (PBUH) are as follows:
We have already shared the biographies of the daughters of Prophet Muhammad (PBUH), and you can read them by clicking the respective names in the list above. In this post, we will briefly talk about the sons of Prophet Muhammad (PBUH).
The Sons of Prophet Muhammad (PBUH)
Qasim ibn Muhammad
The first son of Allah’s Messenger, Prophet Muhammad (PBUH), was Qasim from whom he took his kunyah Abu al-Qasim (the Father of Qasim). Prophet Muhammad (PBUH) liked being called Abu al-Qasim, and his Companions would often call him by this name. 
Narrated Jabi (RA):
A man among us begot a boy whom he named al-Qasim. The people said, “We will not call him (i.e. the father) by that Kunyah (Abu al-Qasim) till we ask the Prophet (PBUH) about it. The Prophet (PBUH) said, “Name yourselves by my name, but do not call (yourselves) by my Kunyah.”
Qasim passed away at very young age in Mecca. He died in 605 CE, even before Prophet Muhammad (PBUH)’s Prophethood.
Abdullah ibn Muhammad
After the birth of Hz Fatima (RA), Prophet Muhammad (PBUH)’s second son, Abdullah was born. There is some difference as to whether he was born after his father’s Prophethood began or before.
Abdullah was also known as al-Tahir and al-Tayyib. He too passed away at a very young age in the year 615 CE.
Ibrahim ibn Muhammad
The last child of Prophet Muhammad (PBUH), Ibrahim, was born in 630 CE or 08 AH. Prophet Muhammad (PBUH) had named him after Prophet Ibrahim (PBUH). As per Arabic tradition of the time, Prophet Muhammad (PBUH) appointed Umm Saif (RA) as the wet nurse of infant Ibrahim. 
Anas bin Malik (RA) reported that Allah’s Messenger (PBUH) said:
“A child was born this night and I named him after the name of my father Ibrahim (PBUH).”
He then sent him to Umm Saif (RA), the wife of a blacksmith who was called Abu Saif (RA).
Prophet Muhammad (PBUH) would often visit their house to see Ibrahim. When the Prophet (PBUH) heard that his son became seriously ill, he went to him with Abd ar-Rahman bin Auf (RA). 
Narrated Anas bin Malik (RA):
We went with Allah’s Messenger (PBUH) to the blacksmith Abu Saif (RA), and he was the husband of the wet-nurse of Ibrahim (the son of the Prophet). Allah’s Messenger (PBUH) took Ibrahim and kissed him and later we entered Abu Saif’s house and at that time Ibrahim was in his last breath, and the eyes of Allah’s Messenger (PBUH) started shedding tears. Abd ar-Rahman bin Auf (RA) said, “O Allah’s Apostle, even you are weeping!” He said, “O Ibn Auf, this is mercy.” Then he wept more and said, “The eyes are shedding tears and the heart is grieved, and we will not say except what pleases our Lord, O Ibrahim! Indeed, we are grieved by your separation.”
Ibrahim passed away at the age of nearly 16 or 18 months in the year 632 CE. Prophet Muhammad (PBUH) led the funeral prayer of his son. He was buried in al-Baqi Cemetery in Medina. 
Narrated Ismail (RA):
I asked Abi Aufa, “Did you see Ibrahim, the son of the Prophet (PBUH)?” He said, “Yes, but he died in his early childhood. Had there been a Prophet after Muhammad, then his son might have lived, but there is no Prophet after him.”
When Ibrahim passed away, the sun was eclipsed. The word went out saying that the solar eclipse had occurred as a result of the sadness over the death of Ibrahim. Upon hearing this, Prophet Muhammad (PBUH) denied such rumors, saying: 
Narrated Abu Bakr (RA):
In the lifetime of the Allah’s Messenger (PBUH), the sun eclipsed and he went out dragging his clothes till he reached the Masjid. The people gathered around him and he led them and offered two rakah of prayers. When the sun (eclipse) cleared, he said, “The sun and the moon are two signs amongst the Signs of Allah; they do not eclipse because of the death of someone, and so when an eclipse occurs, pray and invoke Allah till the eclipse is over.” It so happened that a son of the Prophet (PBUH) called Ibrahim died on that day and the people were talking about that (saying that the eclipse was caused by his death).
- Sahih Bukhari Vol 08, Book 73, Hadith 20
- Sahih Muslim Book 30, Hadith 5733
- Sahih Bukhari Vol 02, Book 23, Hadith 390
- Sahih Bukhari Vol 08, Book 73, Hadith 214
- Sahih Bukhari Vol 02, Book 18, Hadith 170