We have known from our childhood that our holy prophet (sws) had four daughters including Hazrat Fatima, Hazrat Um-e-Kulsoon, Hazrat Ruqaeeya and fourth one I am not sure Hazrat zainab (RA), but recently through one of my shia colleague I got to know that they have the faith that our Prophet had only one daughter Hazrat Fatima (RA). Can you refer to me the Ahadith from Sihah about correct numbers of their family members?
We do not need any Hadith to tell us that the prophet (pbuh) had daughters other than Fatima (ra-ha). The Qur'an testifies to that:
يا أَيُّهَا النَّبِيُّ قُلْ لِأَزْواجِكَ وَ بَناتِكَ وَ نِساءِ الْمُؤْمِنينَ يُدْنينَ عَلَيْهِنَّ مِنْ جَلاَبِيبِهِنَّ ذلِكَ أَدْنى أَنْ يُعْرَفْنَ فَلا يُؤْذَيْنَ وَ كانَ اللَّهُ غَفُوراً رَحيما
"O Prophet! Say to your wives and your daughters and the women of the believers that they let down upon them their over garments. This will be more proper, that they may be known, and thus they will not be given trouble And God is Forgiving, Merciful" (33:59)
Obviously if the prophet (pbuh) only had one daughter then instead of Banatik (plural) we had Bintik (singlular) noun.
Further, in the traditional Shia sources too this fact is well recorded, For instance we read in Muntahi al-A'maal by the very famous Shia scholar, Sheikh Abbas Qumi:
"It is narrated in Qurb al-Asnaad from Imam Sadiq that the messenger (pbuh) had the following children from Khadija: Tahir, Qasim, Fatima, Umme Kulthum, Ruqayye and Zaynab" (Muntahi al-A;maal, chapter 8)