In short, The land of FADAK belonged to Rasoolallah ﷺ as it has to be taken over by the caliph or Leader of his time hence after the death of Saydna Mohammad ﷺ, Sayyidah Fatima رضیﷲ عنها came to Saydna Abu Bakr رضیﷲ عنه and asked for her father's property (FADAK) when Abu bakr became a caliph, however she was unaware that Prophets do not have any inheritance so Abu Bakr told him that Prophets do not leave any inheritance and by default she can not have this land in her property as it belongs to the leader and it's generated income has to be distributed among the muslims as it mentioned in Sunni Hadiths and Shia religion's hadith as well.
We read in al Kafi the Shia book of hadith.
وإن العلماء ورثة الأنبياء إن الأنبياء لم يورثوا دينارا ولا درهما ولكن ورثوا العلم فمن أخذ منه أخذ بحظ وافر.
Imam Jafar Sadiq عليه السلام said Rasoolallah ﷺ said: And the Scholars are the heirs of the Prophets; and the Prophets did not leave dinars and dirhams as inheritance; but they left knowledge. Therefore whosoever takes knowledge has taken a great portion.
Then Fatima رضیﷲ عنها got to know with the content heart and left the place knowing that the land of FADAK belongs to the leader and it's generated amount to be distributed among the people.
What Saydna Abu Bakr رضیﷲ عنه did was to adhere to the saying or hadith of Rasoolallah ﷺ as he wanted to put all of his wealth on the feet of Sayyida Fatima رضیﷲ عنها but he was unable to handover the land of Fadak to her as it belonged to the muslims and Prophets do not have any inheritance to leave for their family according to the hadith which he heard from the mouth of beloved ﷺ.
It is mentioned in Shia book al Furu al Kafi that when Sayyida Fatima asked for Fadak Saydna Abu bakr replied to her.
واموال و احوال خود را از تو مضائقہ نمی آنچه خواہی بگیر تو سیدہ امت پدر خودی شجرہ طیبہ از براۓ فرزندان خود انکار فضل تو کسے نمی تواں کر دو کم تو نافذست در اموال من امادراموال مسلماناں مخالفت گفته پدرتو نمی توانم کرد
I won't hesitate giving my wealth and property to you, you may take what you wish and you're the leader of the ummah of your father and the pious progeny of your sons, no one can deny your virtues and your can have your share in my wealth/property but I can't go against the saying of the Prophet ﷺ in the wealth of the muslims (referring FADAK).
[Furu al Kafi 3/28]
So, Abu Bakr رضیﷲ عنه wished to give all of his wealth to Fatima just like he did with Mohammad ﷺ. once Prophet ﷺ said: The wealth of no one has benefited me as much as the wealth of Abu Bakr so Abu Bakr replied "My life and my wealth are only for you, O Messenger of Allah ﷺ.”
[Musnad Ahmad 7397 sanad classified as Sahih]
