Rasulullah (ﷺ) was very sweet, respectful, and loving towards his daughter Fatima (RA)
Jami` at-Tirmidhi Book 49, Hadith 272
Narrated 'Aishah:

"I have not seen anyone closer in conduct, way, and manners to that of the Messenger of Allah in regards to standing and sitting, than Fatimah the daughter of the Messenger of Allah (ﷺ)." She said "Whenever she would enter upon the Prophet (ﷺ) he would stand to her and kiss her, and he would sit her in his sitting place. Whenever the Prophet (ﷺ) entered upon her she would stand from her seat, and kiss him and sit him in her sitting place. So when the Prophet (ﷺ) fell sick and Fatimah entered, she bent over and kissed him. Then she lifted her head and cried, then she bent over him and she lifted her head and laughed. So I said: 'I used to think that this one was from the most intelligent of our women, but she is really just one of the women.' So when the Prophet (ﷺ) died, I said to her: 'Do you remember when you bent over the Prophet (ﷺ) and you lifted your head and cried, then you bent over him, then you lifted your head and laughed. What caused you to do that?' She said: 'Then, I would be the one who spreads the secrets. He (ﷺ) told me that he was to die from his illness, so I cried. Then he told me that I would be the quickest of his family to meet up with him. So that is when I laughed.'"

حَدَّثَنَا مُحَمَّدُ بْنُ بَشَّارٍ، قَالَ حَدَّثَنَا عُثْمَانُ بْنُ عُمَرَ، قَالَ أَخْبَرَنَا إِسْرَائِيلُ، عَنْ مَيْسَرَةَ ابْنِ حَبِيبٍ، عَنِ الْمِنْهَالِ بْنِ عَمْرٍو، عَنْ عَائِشَةَ بِنْتِ طَلْحَةَ، عَنْ عَائِشَةَ أُمِّ الْمُؤْمِنِينَ، قَالَتْ مَا رَأَيْتُ أَحَدًا أَشْبَهَ سَمْتًا وَدَلاًّ وَهَدْيًا بِرَسُولِ اللَّهِ فِي قِيَامِهَا وَقُعُودِهَا مِنْ فَاطِمَةَ بِنْتِ رَسُولِ اللَّهِ صلى الله عليه وسلم ‏.‏ قَالَتْ وَكَانَتْ إِذَا دَخَلَتْ عَلَى النَّبِيِّ صلى الله عليه وسلم قَامَ إِلَيْهَا فَقَبَّلَهَا وَأَجْلَسَهَا فِي مَجْلِسِهِ وَكَانَ النَّبِيُّ صلى الله عليه وسلم إِذَا دَخَلَ عَلَيْهَا قَامَتْ مِنْ مَجْلِسِهَا فَقَبَّلَتْهُ وَأَجْلَسَتْهُ فِي مَجْلِسِهَا فَلَمَّا مَرِضَ النَّبِيُّ صلى الله عليه وسلم دَخَلَتْ فَاطِمَةُ فَأَكَبَّتْ عَلَيْهِ فَقَبَّلَتْهُ ثُمَّ رَفَعَتْ رَأْسَهَا فَبَكَتْ ثُمَّ أَكَبَّتْ عَلَيْهِ ثُمَّ رَفَعَتْ رَأْسَهَا فَضَحِكَتْ فَقُلْتُ إِنْ كُنْتُ لأَظُنُّ أَنَّ هَذِهِ مِنْ أَعْقَلِ نِسَائِنَا فَإِذَا هِيَ مِنَ النِّسَاءِ فَلَمَّا تُوُفِّيَ النَّبِيُّ صلى الله عليه وسلم قُلْتُ لَهَا أَرَأَيْتِ حِيْنَ أَكْبَبْتِ عَلَى النَّبِيِّ صلى الله عليه وسلم فَرَفَعْتِ رَأْسَكِ فَبَكَيْتِ ثُمَّ أَكْبَبْتِ عَلَيْهِ فَرَفَعْتِ رَأْسَكِ فَضَحِكْتِ مَا حَمَلَكِ عَلَى ذَلِكَ قَالَتْ إِنِّي إِذًا لَبَذِرَةٌ أَخْبَرَنِي أَنَّهُ مَيِّتٌ مِنْ وَجَعِهِ هَذَا فَبَكَيْتُ ثُمَّ أَخْبَرَنِي أَنِّي أَسْرَعُ أَهْلِهِ لُحُوقًا بِهِ فَذَاكَ حِينَ ضَحِكْتُ ‏.‏ قَالَ أَبُو عِيسَى هَذَا حَدِيثٌ حَسَنٌ صَحِيحٌ غَرِيبٌ مِنْ هَذَا الْوَجْهِ وَقَدْ رُوِيَ هَذَا الْحَدِيثُ مِنْ غَيْرِ وَجْهٍ عَنْ عَائِشَةَ ‏.‏
 
Fatima (RA), Chief of the Women of Paradise

Reference: Sahih al-Bukhari 3623

Sahih al-Bukhari 3623
Narrated `Aisha:

Once Fatima came walking and her gait resembled the gait of the Prophet (ﷺ) . The Prophet (ﷺ) said, "Welcome, O my daughter!" Then he made her sit on his right or on his left side, and then he told her a secret and she started weeping. I asked her, "Why are you weeping?" He again told her a secret and she started laughing. I said, "I never saw happiness so near to sadness as I saw today." I asked her what the Prophet (ﷺ) had told her. She said, "I would never disclose the secret of Allah's Messenger (ﷺ)." When the Prophet (ﷺ) died, I asked her about it. She replied. "The Prophet (ﷺ) said: 'Every year Gabriel used to revise the Qur'an with me once only, but this year he has done so twice. I think this portends my death, and you will be the first of my family to follow me.' So I started weeping. Then he said. 'Don't you like to be the chief of all the ladies of Paradise or the chief of the believing women? So I laughed for that."

حَدَّثَنَا أَبُو نُعَيْمٍ، حَدَّثَنَا زَكَرِيَّاءُ، عَنْ فِرَاسٍ، عَنْ عَامِرٍ، عَنْ مَسْرُوقٍ، عَنْ عَائِشَةَ ـ رضى الله عنها ـ قَالَتْ أَقْبَلَتْ فَاطِمَةُ تَمْشِي، كَأَنَّ مِشْيَتَهَا مَشْىُ النَّبِيِّ صلى الله عليه وسلم فَقَالَ النَّبِيُّ صلى الله عليه وسلم ‏ مَرْحَبًا بِابْنَتِي ‏‏.‏ ثُمَّ أَجْلَسَهَا عَنْ يَمِينِهِ أَوْ عَنْ شِمَالِهِ، ثُمَّ أَسَرَّ إِلَيْهَا حَدِيثًا، فَبَكَتْ فَقُلْتُ لَهَا لِمَ تَبْكِينَ ثُمَّ أَسَرَّ إِلَيْهَا حَدِيثًا فَضَحِكَتْ فَقُلْتُ مَا رَأَيْتُ كَالْيَوْمِ فَرَحًا أَقْرَبَ مِنْ حُزْنٍ، فَسَأَلْتُهَا عَمَّا قَالَ‏.‏ فَقَالَتْ مَا كُنْتُ لأُفْشِيَ سِرَّ رَسُولِ اللَّهِ صلى الله عليه وسلم حَتَّى قُبِضَ النَّبِيُّ صلى الله عليه وسلم فَسَأَلْتُهَا فَقَالَتْ أَسَرَّ إِلَىَّ ‏"‏ إِنَّ جِبْرِيلَ كَانَ يُعَارِضُنِي الْقُرْآنَ كُلَّ سَنَةٍ مَرَّةً، وَإِنَّهُ عَارَضَنِي الْعَامَ مَرَّتَيْنِ، وَلاَ أُرَاهُ إِلاَّ حَضَرَ أَجَلِي، وَإِنَّكِ أَوَّلُ أَهْلِ بَيْتِي لَحَاقًا بِي ‏‏‏.‏ فَبَكَيْتُ فَقَالَ ‏ أَمَا تَرْضَيْنَ أَنْ تَكُونِي سَيِّدَةَ نِسَاءِ أَهْلِ الْجَنَّةِ ـ أَوْ نِسَاءِ الْمُؤْمِنِينَ ‏‏.‏ فَضَحِكْتُ لِذَلِكَ‏.‏‏
Reference  : Sahih al-Bukhari 3623
In-book reference  : Book 61, Hadith 129
 
Rasulullah(ﷺ): "Fatima is a part of me, and he who makes her angry, makes me angry."

Reference: Sahih Muslim 2450b

Sahih Muslim 2450b
A'isha reported:

We, the wives of Allah's Apostle (ﷺ), were with him (during his last illness) and none was absent there from that Fatima, who walked after the style of Allah's Messenger (ﷺ), came there, and when he saw her he welcomed her saying: You are welcome, my daughter. He their made her sit on his right side or on his left side. Then he said something secretly to her and she wept bitterly and when he found her (plunged) in grief he said to her something secretly for the second time and she laughed. I ('A'isha) said to her: Allah's Messenger has singled you amongst the women (of the family) for talking (to you something secretly) and you wept. When Allah's Messenger (ﷺ) recovered from illness, I said to her. What did Allah's Messenger (ﷺ) say to you? Thereupon she said: I am not going to disclose the secret of Allah's Messenger (ﷺ). When Allah's Messenger (ﷺ) died, I said to her: I adjure you by the right that I have upon you that you should narrate to me what Allah's Messenger (ﷺ) said to you. She said: Yes, now I can do that (so listen to it). When he talked to me secretly for the first time he informed me that Gabirel was in the habit of reciting the Qur'an along with him once or twice every year, but this year it had been twice and so he perceived his death quite near, so fear Allah and be patient (and he told me) that he would be a befitting forerunner for me and so I wept as you saw me. And when he saw me in grief he talked to me secretly for the second time and said: Fatima, are you not pleased that you should be at the head of the believing women or the head of this Umma? I laughed and it was that laughter which you saw."

حَدَّثَنَا أَبُو كَامِلٍ الْجَحْدَرِيُّ، فُضَيْلُ بْنُ حُسَيْنٍ حَدَّثَنَا أَبُو عَوَانَةَ، عَنْ فِرَاسٍ، عَنْ عَامِرٍ، عَنْ مَسْرُوقٍ، عَنْ عَائِشَةَ، قَالَتْ كُنَّ أَزْوَاجُ النَّبِيِّ صلى الله عليه وسلم عِنْدَهُ لَمْ يُغَادِرْ مِنْهُنَّ وَاحِدَةً فَأَقْبَلَتْ فَاطِمَةُ تَمْشِي مَا تُخْطِئُ مِشْيَتُهَا مِنْ مِشْيَةِ رَسُولِ اللَّهِ صلى الله عليه وسلم شَيْئًا فَلَمَّا رَآهَا رَحَّبَ بِهَا فَقَالَ ‏"‏ مَرْحَبًا بِابْنَتِي ‏"‏ ‏.‏ ثُمَّ أَجْلَسَهَا عَنْ يَمِينِهِ أَوْ عَنْ شِمَالِهِ ثُمَّ سَارَّهَا فَبَكَتْ بُكَاءً شَدِيدًا فَلَمَّا رَأَى جَزَعَهَا سَارَّهَا الثَّانِيَةَ فَضَحِكَتْ ‏.‏ فَقُلْتُ لَهَا خَصَّكِ رَسُولُ اللَّهِ صلى الله عليه وسلم مِنْ بَيْنِ نِسَائِهِ بِالسِّرَارِ ثُمَّ أَنْتِ تَبْكِينَ فَلَمَّا قَامَ رَسُولُ اللَّهِ صلى الله عليه وسلم سَأَلْتُهَا مَا قَالَ لَكِ رَسُولُ اللَّهِ صلى الله عليه وسلم قَالَتْ مَا كُنْتُ أُفْشِي عَلَى رَسُولِ اللَّهِ صلى الله عليه وسلم سِرَّهُ ‏.‏ قَالَتْ فَلَمَّا تُوُفِّيَ رَسُولُ اللَّهِ صلى الله عليه وسلم قُلْتُ عَزَمْتُ عَلَيْكِ بِمَا لِي عَلَيْكِ مِنَ الْحَقِّ لَمَا حَدَّثْتِنِي مَا قَالَ لَكِ رَسُولُ اللَّهِ صلى الله عليه وسلم فَقَالَتْ أَمَّا الآنَ فَنَعَمْ أَمَّا حِينَ سَارَّنِي فِي الْمَرَّةِ الأُولَى فَأَخْبَرَنِي ‏"‏ أَنَّ جِبْرِيلَ كَانَ يُعَارِضُهُ الْقُرْآنَ فِي كُلِّ سَنَةٍ مَرَّةً أَوْ مَرَّتَيْنِ وَإِنَّهُ عَارَضَهُ الآنَ مَرَّتَيْنِ وَإِنِّي لاَ أُرَى الأَجَلَ إِلاَّ قَدِ اقْتَرَبَ فَاتَّقِي اللَّهَ وَاصْبِرِي فَإِنَّهُ نِعْمَ السَّلَفُ أَنَا لَكِ ‏"‏ ‏.‏ قَالَتْ فَبَكَيْتُ بُكَائِي الَّذِي رَأَيْتِ فَلَمَّا رَأَى جَزَعِي سَارَّنِي الثَّانِيَةَ فَقَالَ ‏"‏ يَا فَاطِمَةُ أَمَا تَرْضَىْ أَنْ تَكُونِي سَيِّدَةَ نِسَاءِ الْمُؤْمِنِينَ أَوْ سَيِّدَةَ نِسَاءِ هَذِهِ الأُمَّةِ ‏"‏ ‏.‏ قَالَتْ فَضَحِكْتُ ضَحِكِي الَّذِي رَأَيْتِ ‏.‏
Reference  : Sahih Muslim 2450b
In-book reference  : Book 44, Hadith 143