Is it true that Hazrat Aisha RA died in 50 hijri at the age of 64 to 67? What narrations and ahadith prove it?
First I don't know where you've got the information that the mother of believers 'Aisha'h bint abi Bakr () died 50 a.H. I couldn't make out any source saying so.
Secondly as her death has been after the death of our prophet () any source or narration that may tell us a date is strictly speaking not a hadith, but an athar or khabar. Imam al-Bukhari (for example) quoted two narrations in his Sahih which seem to refer to her last days:
Once `Aisha became sick and Ibn 'Abbas went to see her and said, "O mother of the believers! You are leaving for truthful fore-runners i.e. for Allah's Messenger (ﷺ) and Abu Bakr. (Sahih al-Bukhari)
Ibn 'Abbas asked permission to visit Aisha before her death, and at that time she was in a state of agony. She then said. "I am afraid that he will praise me too much." And then it was said to her, "He is the cousin of Allah's Messenger (ﷺ) and one of the prominent Muslims." Then she said, "Allow him to enter." (When he entered) he said, "How are you?" She replied, "I am Alright if I fear (Allah)." Ibn 'Abbas said, "Allah willing, you are Alright as you are the wife of Allah's Messenger (ﷺ) and he did not marry any virgin except you and proof of your innocence was revealed from the Heaven." Later on Ibn Az-Zubair entered after him and 'Aisha said to him, "Ibn 'Abbas came to me and praised me greatly, but I wish that I was a thing forgotten and out of sight." (Sahih al-Bukhari)
It was also narrated that she wanted to be buried beside her husband and his two companions, but after that -seemingly due to the circumstances of the battle of the camel- decided to be buried with the prophets () other wives. So she was buried in al-Baqi'i (See here in al-Mustadrak المستدرك على الصحيحين of al-Hakim from Nishapure).
Quotes from historical sources
Any source quoting her date of death would rather be a book on biographies or history. Imam a-Dhahabi in his Siyar a'alaam an-Nubala' سير أعلام النبلاء quoted a few narrations on this -with comments on wrong narrations-:
In the following I will translate from Arabic language, as these translations are of my own take them carefully
قال محمد بن عمر : حدثنا ابن جريج ، عن نافع ، قال : شهدت أبا هريرة صلى على عائشة بالبقيع ، وكان خليفة مروان على المدينة ، وقد اعتمر تلك الأيام .
Muhammad ibn 'Unmar said: We narrated from ibn Juraij from Nafi' who said: I witnessed abu Hurrirah leading the prayer of funeral for 'Aisha in al-Baqi'i, and at the time governer of Meidna was Marwan and he was performing 'Umrah these days.
قال عروة بن الزبير : دفنت عائشة ليلا .
'Urwa ibn az.Zubayr said: she was buried by night.
قال هشام بن عروة ، وأحمد بن حنبل ، وشباب وغيرهم : توفيت سنة سبع وخمسين . Hisham ibn 'Urwa, Ahmad ibn Hanbal, Shabab and other said: She died in the year 57 a.H..
وقال أبو عبيدة معمر بن المثنى ، والواقدي ، وغيرهما : سنة ثمان وخمسين .
While abu 'Obyadah Ma'amar ibn al-Muthannah, al-Waqidi (the historian) and other said: at the year 58 a.H..
قال الواقدي : حدثنا ابن أبي سبرة ، عن موسى بن ميسرة عن سالم سبلان : أنها ماتت في الليلة السابعة عشرة من شهر رمضان بعد الوتر ، فأمرت أن تدفن من ليلتها ، فاجتمع الأنصار ، وحضروا ، فلم ير ليلة أكثر ناسا منها . نزل أهل العوالي ، فدفنت بالبقيع . Al-Waqidi said: We narrated from ibn abi Sabrah from Musah ibn Mysarah from Salim Sabalaan: that she died at the 17th night of Ramadan after the witr prayer, and she ordered to be buried at the same night, the Ansaar gathered and came, and no similar night has been witnessed where so many people gathered, the people of al-'Awali (surroundings of Medina) came too and she was buried in al-Baqi'i.
وقد قيل : إنها مدفونة بغربي جامع دمشق . وهذا غلط فاحش ، لم تقدم رضي الله عنها - إلى دمشق أصلا ، وإنما هي مدفونة بالبقيع .
ومدة عمرها : ثلاث وستون سنة وأشهر . (Source: Siya A'alam an-Nubala')
It was said: She was buried at the west of the mosque of Damascus. And this is an awful mistake, as she never ever moved to Damsuscus at allm but she is buried in al-Baqi'i.
And the time of her life was of 63 years and a few months.
Ibn Kathir in his al-Bidaya wa an-Nihaya البداية والنهاية quoted three opinions on the date of her death 57 a.H., 58 a.H. and 59 a.H.:
وَقَدْ كَانَتْ وَفَاتُهَا فِي هَذَا الْعَامِ سَنَةَ ثَمَانٍ وَخَمْسِينَ وَقِيلَ قَبْلَهُ بِسَنَةٍ، وَقِيلَ بَعْدَهُ بِسَنَةٍ، وَالْمَشْهُورُ فِي رَمَضَانَ مِنْهُ وَقِيلَ فِي شَوَّالٍ، وَالْأَشْهَرُ لَيْلَةَ الثُّلَاثَاءِ السَّابِعُ عَشَرَ مِنْ رَمَضَانَ، وَأَوْصَتْ أَنْ تُدْفَنَ بِالْبَقِيعِ لَيْلًا، وَصَلَّى عَلَيْهَا أَبُو هُرَيْرَةَ بَعْدَ صَلَاةِ الْوِتْرِ،
And her death was in this year 58 a.H. and it was said one year earlier and also one year later, and the commonly known (mashhur) is that she died in Ramadan and some said Shawwal, and the most common was the night of Tuesday the 17th day of Ramadan, and her last will was to be buried in al-Baqi'i at night and abu Hurrairah lead the funeral prayer after praying witr.
وَنَزَلَ فِي قَبْرِهَا خَمْسَةٌ، وَهُمْ عَبْدُ اللَّهِ وَعُرْوَةُ ابْنَا الزُّبَيْرِ بْنِ الْعَوَّامِ، مِنْ أُخْتِهَا أَسْمَاءَ بِنْتِ أَبِي بَكْرٍ، وَالْقَاسِمُ وَعَبْدُ اللَّهِ ابْنَا أَخِيهَا مُحَمَّدِ بْنِ أَبِي بَكْرٍ، وَعَبْدِ اللَّهِ بْنِ عَبْدِ الرَّحْمَنِ بْنِ أَبِي بَكْرٍ،
Five people went down to her grave these were: 'Abdullah and 'Urwa the sons of az-Zubayr ibn al-'Awwam, (children) of her sister Asma' daughter of abu Bakr, Al_Qassim and 'BAdullah the two sons of her brother Muhammad son of abu BAkr, And 'Abdullah ibn 'Abdurrahman ibn abu Bakr.
وَكَانَ عُمْرُهَا يَوْمَئِذٍ سَبْعًا وَسِتِّينَ سَنَةً، لِأَنَّهُ تُوُفِّيَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وعمرها ثمان عَشْرَةَ سَنَةً، وَكَانَ عُمْرُهَا عَامَ الْهِجْرَةِ ثَمَانِ سنين أو تسع سنين، فالله أعلم ورضي الله تعالى عن أبيها وعن الصحابة أجمعين. (Source al-Bidaya wa an-Nihaya)
And her age at the time was of 67 years, as the Prophet Allahs prayers and blessings be upon him died and she was 18 years old, and her age in the year of Hijra was 8 or 9 years, so Allah knows best and may be pleased with her father and all the companions.
So basically you may find as a date of death the year 57 a.H., 58 a.H. or 59 a.H. the majority holds the opinion that she died in the night of a Tuesday corresponding to the 17th day of Ramadan in that year, some say it was in Shawwal. As for her age at her time of death was of 67 or 63 years.