It was narrated from Abu Salamah that Fatimah said to Abu Bakr:

Who will inherit from you if you die? He Said: My children and my wife. She said: Then why can't we inherit from the Prophet (ﷺ). He said: I heard the Prophet (ﷺ) say: `The Prophet (ﷺ) is not to be inherited from.” But I will sponsor those whom the Messenger of Allah (ﷺ) used to sponsor and I will spend on those on whom the Messenger of Allah used to spend.

حَدَّثَنَا عَفَّانُ، حَدَّثَنَا حَمَّادُ بْنُ سَلَمَةَ، عَنْ مُحَمَّدِ بْنِ عَمْرٍو، عَنْ أَبِي سَلَمَةَ، أَنَّ فَاطِمَةَ، رَضِيَ اللَّهُ عَنْهَا قَالَتْ لِأَبِي بَكْرٍ مَنْ يَرِثُكَ إِذَا مِتَّ قَالَ وَلَدِي وَأَهْلِي قَالَتْ فَمَا لَنَا لَا نَرِثُ النَّبِيَّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ سَمِعْتُ النَّبِيَّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يَقُولُ إِنَّ النَّبِيَّ لَا يُورَثُ وَلَكِنِّي أَعُولُ مَنْ كَانَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يَعُولُ وَأُنْفِقُ عَلَى مَنْ كَانَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يُنْفِقُ‏.‏