Narrated 'Aisha:

Fatima sent somebody to Abu Bakr asking him to give her her inheritance from the Prophet from what Allah had given to His Apostle through Fai (i.e. booty gained without fighting). She asked for the Sadaqa (i.e. wealth assigned for charitable purposes) of the Prophet at Medina, and Fadak, and what remained of the Khumus (i.e., one-fifth) of the Khaibar booty. Abu Bakr said, "Allah's Apostle ﷺ said, 'We (Prophets), our property is not inherited, and whatever we leave is Sadaqa, but Muhammad's Family can eat from this property, i.e. Allah's property, but they have no right to take more than the food they need.' By Allah! I will not bring any change in dealing with the Sadaqa of the Prophet (and will keep them) as they used to be observed in his (i.e. the Prophet's) life-time, and I will dispose with it as Allah's Apostle used to do," Then 'Ali said, "I testify that None has the right to be worshipped but Allah, and that Muhammad is His Apostle," and added, "O Abu Bakr! We acknowledge your superiority." Then he (i.e. 'Ali) mentioned their own relationship to Allah's Apostle and their right. Abu Bakr then spoke saying, "By Allah in Whose Hands my life is. I love to do good to the relatives of Allah's Apostle rather than to my own relatives"

حَدَّثَنَا أَبُو الْيَمَانِ، أَخْبَرَنَا شُعَيْبٌ، عَنِ الزُّهْرِيِّ، قَالَ حَدَّثَنِي عُرْوَةُ بْنُ الزُّبَيْرِ، عَنْ عَائِشَةَ، أَنَّ فَاطِمَةَ ـ عَلَيْهَا السَّلاَمُ ـ أَرْسَلَتْ إِلَى أَبِي بَكْرٍ تَسْأَلُهُ مِيرَاثَهَا مِنَ النَّبِيِّ ﷺ فِيمَا أَفَاءَ اللَّهُ عَلَى رَسُولِهِ ﷺ، تَطْلُبُ صَدَقَةَ النَّبِيِّ ﷺ الَّتِي بِالْمَدِينَةِ وَفَدَكٍ وَمَا بَقِيَ مِنْ خُمُسِ خَيْبَرَ. فَقَالَ أَبُو بَكْرٍ إِنَّ رَسُولَ اللَّهِ ﷺ قَالَ
" لاَ نُورَثُ، مَا تَرَكْنَا فَهْوَ صَدَقَةٌ، إِنَّمَا يَأْكُلُ آلُ مُحَمَّدٍ مِنْ هَذَا الْمَالِ ـ يَعْنِي مَالَ اللَّهِ ـ لَيْسَ لَهُمْ أَنْ يَزِيدُوا عَلَى الْمَأْكَلِ ". وَإِنِّي وَاللَّهِ لاَ أُغَيِّرُ شَيْئًا مِنْ صَدَقَاتِ النَّبِيِّ ﷺ الَّتِي كَانَتْ عَلَيْهَا فِي عَهْدِ النَّبِيِّ ﷺ، وَلأَعْمَلَنَّ فِيهَا بِمَا عَمِلَ فِيهَا رَسُولُ اللَّهِ ﷺ. فَتَشَهَّدَ عَلِيٌّ، ثُمَّ قَالَ إِنَّا قَدْ عَرَفْنَا يَا أَبَا بَكْرٍ فَضِيلَتَكَ. وَذَكَرَ قَرَابَتَهُمْ مِنْ رَسُولِ اللَّهِ ﷺ وَحَقَّهُمْ. فَتَكَلَّمَ أَبُو بَكْرٍ فَقَالَ وَالَّذِي نَفْسِي بِيَدِهِ، لَقَرَابَةُ رَسُولِ اللَّهِ ﷺ أَحَبُّ إِلَىَّ أَنْ أَصِلَ مِنْ قَرَابَتِي.