We find in many narrations that Imam Hussain (a.s) had many daughters named Fatimah,
1. One is the eldest Fatima of the daughters of Imam Hussain (a.s). She was the daughter who was given an important document by her father Imam Hussain (a.s) was he was going for martyrdom on the day of Ashura. She gave what was given to her to Imam Ali ibn Hussain Zainul Abideen (a.s). This is mentioned in al-Kafi (volume 1, page 303).
2. Another daughter is Fatima bint al-Hussain, who was the wife of al-Hasan al-Muthanna, who is son of Imam Hasan (a.s) and her mother is Umm Isaaq. She was a very pious and very learned lady, who has also narrated many narrations in our books.
She was in Karbala, and was arrested by the enemies and the narration of her suffering is mentioned in Amaali al-Sadooq (page 227).
She gave a sermon which is mentioned in many books. It was narrated by al-Tabrisi in his book al-Ehtijaj (volume 2, page 27).
This Fatima bint Hussain narrated from Asmaa' bint Umais the narration of 'Radd ash Shams' - the return of the sun for Amir al-Mumineen (a.s), as it is mentioned in the book of Sheikh al-Sadooq, Man la Yahdaruhul Faqih (volume 4, page 439).
She was the Daughter of Imam Hussain (a.s) who had the incident in Shaam (Syria) when one of the people of Shaam asked Yazeed to give him
It is mentioned in Kitab al-Irshad by Sheikh al-Mufid (volume 2, page 121). In Basar al-Darajat by al-Saffar (page 205), it is mentioned that this lady (i.e, Fatima) had some important items from the Prophet Muhammad (saw), and also it is in the book al-Iqbal by ibn Tawoos (volume 3, page 86) that her father Imam Hussain (a.s) informed her about what will happen to some of her children.
3. Another daughter of Imam Hussain (a.s) is Fatima al-Aleela who was left in Madina al Munawara because she was not well.
Allama al-Majlisi in Bihar ul Anwar, al-Khawarizmi (Sunni scholar), ibn Asaaqir (Sunni scholar) and ibn al-Adeem (Sunni scholar) all narrated a narration to al-Mufaddal bin Omer al-Juffi from Imam al-Sadiq (a.s) who received it from his father Imam al-Baqir (a.s), who received it from his father Imam Ali ibn Hussain Zainul Abideen (a.s) that when Imam Hussain (a.s) was killed in Karbala, Ghurab (the black bird) came from Karbala to Madina with some of the blood of Imam Hussain (a.s) and went on the wall of the house where Fatima bint Hussain was. When she saw the bird with the blood, she started crying on her father.
This is mentioned in Bihar al Anwar (volume 45, page 172), in Tarikh Madina Dimishq by ibn Asaakir (volume 70, page 24), in al-Talab fi Tarikh Hallab by ibn al-Adeem (volume 6, page 2647) and in al-Hussain by al-Khawarizmi (chapter 12).
This is some of what we have now about Fatima al-Aleela (a.s).