The following ahaadeeth about the virtues of Soorat Ta-Ha are saheeh:
It was narrated that ‘Abd-Allaah ibn Mas’ood (may Allaah be pleased with him) said concerning Bani Israa’il (al-Isra’), al-Kahf, Maryam, Ta-Ha and al-Anbiya’: They are among the best of the earliest ones that I learned by heart.
Narrated by al-Bukhaari (4994).
Al-Bayhaqi said in Shu’ab al-Eemaan:
He was referring to the superiority of these soorahs because of what they contain of stories of the Prophets (blessings and peace be upon them) and the nations.
And they were among the first soorahs to be revealed at the beginning of Islam, because they are Makkan soorahs, and they were among the first parts of the Qur'aan to be recited and memorized. End quote.
Al-Haafiz Ibn Hajar said in Fath al-Baari (8/388):
What Ibn Mas’ood meant was that they were among the first parts of the Qur’aan that he learned, and that they have a special virtue because they contain stories of the Prophets and the nations. End quote.
It was narrated from Abu Umaamah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The greatest name of Allaah appears in three soorahs of the Qur’aan: in al-Baqarah, Aal ‘Imraan and Ta-Ha.”
Narrated by Ibn Majaah (3856) and al-Haakim (1/686); classed as hasan by al-Albaani in al-Silsilah al-Saheehah (746).
He (may Allaah have mercy on him) said:
With regard to the words of al-Qaasim ibn ‘Abd al-Rahmaan (the one who narrated it from Abu Umaamah) that the greatest name is found in the verse (interpretation of the meaning): “And (all) faces shall be humbled before (Allaah), Al-Hayyul-Qayyum (the Ever Living, the One Who sustains and protects all that exists)” [Ta-Ha 20:111] in Soorat Ta-Ha, I could not find anything to support it. It is more likely in my view that it is in the verse at the beginning of the soorah: “Verily, I am Allaah! Laa ilaaha illa Ana (none has the right to be worshipped but I)” [Ta-Ha 20:14], and that is in accordance with some saheeh ahaadeeth. See: al-Fath (11/225) and Saheeh Abi Dawood (1341). End quote.
Concerning the virtues of Soorat Ta-ha there are some da’eef (weak) ahaadeeth, which I will quote here to draw attention to them and warn people against them.
It was narrated that Abu Hurayrah said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said:
“Allaah, may He be blessed and exalted, recited Ta-Ha and Ya-Seen one thousand years before He created the heavens and the earth, and when the angels heard the Qur'aan they said: Glad tidings to the nation to whom this is revealed, glad tidings to the hearts that carry this, glad tidings to the tongues that speak it.”
Narrated by al-Daarimi (2/547). The editor said: Its isnaad is very weak. Ahmad said of ‘Umar ibn Hafs ibn Dhakwaan: We rejected his hadeeth and regarded him as very weak. In al-Mu’jam al-Awsat (5/133) it says: Ibn Hibbaan said in al-Majrooheen (1/208): This is a fabricated text. Ibn al-Jawzi said likewise in al-Mawdoo’aat (1/110). Ibn Katheer said in Tafseer al-Qur’aan il-Azeem (5/271): It is weird. Al-Albaani said in al-Silsilah al-Da’eefah (1248): It is munkar. See also al-Kaamil (1/216) and Lisaan al-Meezaan (1/114).
It was narrated that Ma’qil ibn Yasaar (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said:
“Learn the Qur'aan, accept as permissible what it permits, regard as forbidden what it forbids, follow its guidance and do not reject anything in it. Whatever you are confused about in it, refer it to Allaah and to those who are in authority after I am gone, so that they may tell you. Believe in the Tawraat and Injeel and Zaboor, and what the Prophets brought from their Lord, but be content with the Qur’aan and what it contains of clarity, for it is an intercessor whose intercession will be accepted. Each verse will have light on the Day of Resurrection. I have been given Soorat al-Baqarah among the early Revelation, and I have been given Ta-Ha and Ta-Seen-Meems and Ha-Meems from the tablets of Moosa and I have been given the Opening of the Book (al-Faatihah) from beneath the Throne.
Narrated by al-Haakim in al-Mustadrak (1/757) and he said: This hadeeth has a saheeh isnaad although they (al-Bukhaari and Mulsim) did not narrate it. Also narrated by al-Tabaraani in al-Mu’jam al-Kabeer (20/225). Classed as da’eef by al-Albaani in al-Silsilah al-Da’eefah (2826) and by Ibn Hibbaan in al-Majrooheen (2/65).
That the Prophet (peace and blessings of Allaah be upon him) used to say in his du’aa’:
“O Lord of Ta-Ha and Yaa-Seen, O Lord of the Holy Qur’aan.”
Ibn Taymiyah (may Allaah have mercy on him) said in Majmoo’ al-Fataawa (5/173-174):
There is no difference of opinion among the scholars that this hadeeth is a lie against the Messenger of Allaah (peace and blessings of Allaah be upon him). End quote.
“Whoever reads Ta-Ha will be given the reward of the Muhaajireen and Ansaar on the Day of Resurrection.”
This was quoted by al-Zamakhshari and al-Baydaawi with regard to the virtues of Soorat Ta-Ha, but it is a fabricated hadeeth.
See: al-Kashf al-Ilaahi by al-Tarabulsi (1/178).
With regard to what you asked about the virtue of reading it three times every night, I could not find that in the books of the Sunnah, and I did not even find it in the books of mawdoo’ (fabricated) reports. Nothing concerning that has been proven from the Prophet (peace and blessings of Allaah be upon him), so you should be careful and avoid that, and strive to follow the saheeh Sunnah of the Prophet (peace and blessings of Allaah be upon him), and shun that which is da’eef (weak) and mawdoo’ (fabricated).
And Allaah knows best.