The question of how many daughters the Prophet Muhammad (peace be upon him and his Progeny) had, has come from some people, who wanted to attribute the lineage of the Prophet’s fostered daughters to the lineage of the Prophet’s real daughter.
The people in Jahiliyah (Before Islam) had the same way of thinking as these people do. The people in Jahiliyah also used to attribute the lineage of fostered children to the lineage of their guardians, and mistakenly claim they all equal children.
That’s why it is well known that Prophet’s fostered son, Zaid Bin Harithah , used to be called “Zaid ibn Muhammad” by some people, even though Zaid was never the Prophet’s son at all but son of Harithah.
It was for that very reason that Allah ordered the Prophet to get married to Zainab bint Jahsh, who was the ex-wife of Zaid. This was to correct the Jahili thinking that the fostered son is like the real son.
“O Prophet, remember when you said to the one (Zaid) whom Allah as well as you had favored: "Keep your wife in wedlock and fear Allah". You sought to hide in your heart what Allah intended to reveal; you were afraid of the people whereas it would have been more appropriate to fear Allah. So when Zaid divorced his wife, We gave her to you in marriage, so that there remains no hindrance for the believers to wed the wives of their adopted sons if they divorced them. And Allah's Command had to be carried out.”
-Surah Al Ahzab, Ayah 37
From the same origin of misunderstanding, some people claimed that the Prophet had 3 daughters prior to Fatima being born. However, this is a misconception as these 3 daughters were his fostered daughters while Fatima was his real biological daughter.
Here are some facts to clarify this misunderstanding;
1. Lady Khadijah had a sister by the name of Haala bint Khuwailid. Haala had 3 daughters whose names were Zainab, Rukhaiya & Umm Kulthum (Manaaqib aal Abi Talib, volume 1, page 162).
Even some of the historians have stated that Zainab & Rukhaiya were the daughters of Haala's husband from another wife (not Hala), but both mother and father died, so Khadijah adopted them (Al-Istigatha by Al-Kufi, volume 1, page 68).
All of the authentic evidences make it very clear that all of the Prophet’s children were born after The Bi'atha/declaration of Prophet hood (see Al Bad' Wal Tarikh البدء والتاريخ , volume 5, page 16, Nasib Quraysh نسب قريش Volume 21, Al Mawahib Al Laduniyya, المواهب اللدنية volume 1, page 196, Tareek Al Khamis تاريخ الخميس , volume 1, page 272, Majma Al Zawaid مجمع الزوائد , volume 9, page 217, Al Bidaiya Wal Nihaiya البداية والنهاية , volume 12, page 294, Al Seerah Al Halabiyyah السيرة الحلبية , volume 3, page 308)
Zainab & Rukhaiya, the fostered daughters of Khadija were married to 2 sons of Abu Lahab, then they got divorced from them. One of them eventually got married to Uthmaan.
That proves that they were not the real daughters of the Prophet because all of the Prophet’s children were born after Bi'tha/declaration of Prophet hood.
Some people claim that these 3 daughters were Khadijah’s own daughters from a previous marriage. However, this claim of a "previous' marriage is doubtful because the narrations which state that Khadijah had a husband before she was married to the Prophet, were fabricated by supporters of Bani Ummaiya in an attempt lower the status of Lady Khadijah.
The authentic evidence shows us that Lady Khadijah refused all marriage proposals from the leaders of society at that time and that she was only ever married to the Prophet, peace be upon him and all his noble family.
Many authentic historians and scholars like Ibn Shar Ashub ابن شهر آشوب , Ahmed Al Balathoreeأحمد البلاذري , Abul Qasim al Kufi أبو القاسم الكوفي , Al Mortatha السيد المرتضى in his book “Al-Shaafi” and Abu Jafar in his book “Al-Talkees”التلخيص , have confirmed that Lady Khadijah got married to the Prophet when she was a virgin.
In the well-known authentic sermon of Fatima a.s, in the Masjid of the Prophet, in front of a big number of Muslims, she said “The Prophet is my father and never the father of any other woman”. This means that she was affirming that she was the Prophet’s only real daughter.
In the book Sahih Al Bukari, volume 3, page 68, there is a clear evidence that Ali was the only son-in-law of the Prophet and Uthmaan was not.
These are a few points to confirm that Fatima a.s was the only real daughter of the Prophet.
No need to mention the emphasis of the Prophet in telling the people to be just when dealing with their daughters and sons and to treat them fairly and equally. Seeing as this is the case, why would the Prophet focus only on Fatima, in all of the Hadith that have been recorded about his gifting Fadak to her and only her? There is no mention of these other fostered daughters.
This itself is a further evidence that Fatima was the Prophet’s only daughter while the others were fostered by him and his wife Khadija.