Lady Zainab was (accurately) the third child born
to Lady Fatima Zahra (A). In other words, she was born directly after Imam
Hussain (A); despite the false claim of some historians who hold the opinion
that Zainab was born after the miscarriage, which Lady Fatima had and resulted
in the martyrdom of Mohsin. These historians are motivated by their desire
to divert the attention from the merciless attack on Lady Fatima's house
which not only resulted in Mohsin's martyrdom, but also in the eventual
death of Lady Fatima herself.
Among these writers is the Egyptian Bint Ash-Shati who wrote in her book Batlat Karbala:
"Zahra, the Prophet's daughter was about to give
birth to a new baby after bringing happiness unto Messenger's life by giving
birth to his beloved sons: Al-Hassan and Al-Hussain, and a third child,
who was not destined to live and whose name was to be Mohsin Ibn Ali..." 
Regardless of these unfounded claims, it has been
established that Lady Zainab (A) was born in 5 A.H., and that she was the
third child of the honorable Alawi household.
It is said that her grandfather, the Prophet named her Zainab that is derived from two words: "Zain" and "Ab" that together means "The embellishment of her father." Yet, Muhammad Jawad Mughniah quoted the Egyptian newspaper, Al-Jomhuria dated October 31, 1972, in his book Al-Hussain Batala Karbala as saying:
"Zainab was born in Shaban 5 A.H. When her mother
brought her to Imam Ali (may Allah be pleased with him) and said: "Name
her" he replied: "I would not name her before Allah's Messenger." At this
time the Prophet was on a trip and when he returned, he again refused to
name her before her Lord. So Gabriel descended to inform the Prophet about
Allah's blessings and said: "The name of this baby is Zainab; Allah
chose this name for her."
Zainab's history itself speaks of her honorable life
and noble traits, as well as the miseries she encountered during her childhood,
such as the death of her great grandfather, the martyrdom of her mother
(A), and the various inflictions which she lived through during the quarter
of a century that her father, Imam Ali (A), was confined to his house as
a result of his rights having been usurped by others.
Moreover, when Zainab emigrated from Medina to Kufa,
her Father's capital then, several misfortunes were destined for her; starting
with the martyrdom of Imam Ali (A). This was followed by fierce battles
between her brother, Al-Hassan, and Mu'awiya, which resulted in the poisoning
of the Imam (A). After several years, Zainab faced the greatest disaster
of history when Imam Hussain along with the prominent Hashimite men were
massacred at Karbala by the Umayyads. After massacring the men, Zainab
and the women were taken to Syria, but she did not panic nor did she give
into the enemy. From Syria she was sent to Medina and then exiled to Egypt
to live the rest of her life.
Zainab's tomb is well-known in Egypt today and is visited by believers from all over the world. (There is disagreement about the location of Zainab's tomb; it is believed by most to be located in Syria.) (compiler's note)
 Bihar: v.10.