Virtues of Surah Taha
Question

I would like to find out about the virtue of reading Surah Taha, and the virtue of reading it every night three times in succession for a certain period. Thank you very much.
Praise be to Allah.Authentic hadith about the merits of Surah Taha
The following hadiths about the virtues of Surah Taha are sahih (authentic): 
1- ‘Abd-Allah ibn Mas’ud (may Allah be pleased with him) said concerning Bani Israil (al-Isra), al-Kahf , Maryam, Taha and al-Anbiya: They are among the best of the earliest ones that I learned by heart. (Narrated by al-Bukhari, 4994)
Al-Bayhaqi said in Shu’ab al-Iman:  
“He was referring to the superiority of these surahs because of what they contain of stories of the prophets (peace and blessings be upon them) and the nations. 
And they were among the first surahs to be revealed at the beginning of Islam, because they are Makkan surahs, and they were among the first parts of the Quran to be recited and memorized.”
Al-Hafiz Ibn Hajar said in Fath al-Bari (8/388): 
“What Ibn Mas’ud (may Allah be pleased with him) meant was that they were among the first parts of the Quran that he learned, and that they have a special virtue because they contain stories of the prophets (peace and blessing be upon them) and the nations.”
2- Abu Umamah (may Allah be pleased with him) narrated that the Messenger of Allah (peace and blessings of Allah be upon him) said: “The greatest name of Allah appears in three surahs of the Quran: in al-Baqarah , Al ‘Imran and Taha.” (Narrated by Ibn Majah (3856) and al-Hakim (1/686); classed as hasan (sound) by al-Albani in al-Silsilah al-Sahihah (746) 
 Al-Albani (may Allah have mercy on him) said: 
“With regard to the words of al-Qasim ibn ‘Abd al-Rahman (the one who narrated it from Abu Umamah) that the greatest name is found in the verse (interpretation of the meaning):  “And (all) faces shall be humbled before (Allah), Al-Hayyul-Qayyum (the Ever Living, the One Who sustains and protects all that exists)” [Taha20:111] in Surah Taha, 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 Surah: “Verily, I am Allah! La ilaha illa Ana (none has the right to be worshipped but I)” [Taha 20:14], and that is in accordance with some sahih hadiths (authentic narrations. See: al-Fath (11/225) and Sahih Abi Dawud (1341).” 
Weak hadiths about the virtues of Surah Taha
Concerning the virtues of Surah Taha there are some da’if (weak) hadiths, which I will quote here to draw attention to them and warn people against them. 
1- Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said:
“Allah, may He be blessed and exalted, recited Taha and Yasin one thousand years before He created the heavens and the earth, and when the angels heard the Quran 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-Darimi (2/547). The editor said: Its isnad (chain of narrators) is very weak. Ahmad said of ‘Umar ibn Hafs ibn Dhakwan: We rejected his hadith and regarded him as very weak. In al-Mu’jam al-Awsat (5/133) it says: Ibn Hibban said in al-Majruhin (1/208): This is a fabricated text. Ibn al-Jawzi said likewise in al-Mawdu’at (1/110). Ibn Kathir said in Tafsir al-Quran il-Azim (5/271): It is weird. Al-Albani said in al-Silsilah al-Da’ifah (1248): It is munkar (denounced). See also al-Kamil (1/216) and Lisan al-Mizan (1/114). 
2- Ma’qil ibn Yasar (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said:
“Learn the Quran, 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 Allah and to those who are in authority after I am gone, so that they may tell you. Believe in the Tawrat and Injil and Zabur , and what the prophets brought from their Lord, but be content with the Quran 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 Surah al-Baqarah among the early Revelation, and I have been given Taha and Tasin-Meems and Ha-Meems from the tablets of Musa and I have been given the Opening of the Book (al-Fatihah) from beneath the Throne. 
Narrated by al-Hakim in al-Mustadrak (1/757) and he said: This hadith has a sahih isnad although they (al-Bukhari and Mulsim) did not narrate it. Also narrated by al-Tabarani in al-Mu’jam al-Kabir (20/225). Classed as da’if by al-Albani in al-Silsilah al-Da’ifah (2826) and by Ibn Hibban in al-Majruhin (2/65). 
3- Prophet Muhammad (peace and blessings of Allah be upon him) used to say in his du’a (supplication):
“O Lord of Taha and Yasin, O Lord of the Holy Quran.” 
Ibn Taymiyah (may Allah have mercy on him) said in Majmu’ al-Fatawa (5/173-174): 
There is no difference of opinion among the scholars that this hadith is a lie against the Messenger of Allah (peace and blessings of Allah be upon him). End quote. 
4- “Whoever reads Taha will be given the reward of the Muhajirin (Emigrants) and the Ansar (Helpers) on the Day of Resurrection.” 
This was quoted by al-Zamakhshari and al-Baydawi with regard to the virtues of Surah Taha, but it is a fabricated hadith. See, al-Kashf al-Ilahi by al-Tarabulsi (1/178). 
Is there any virtue for reading Surah Taha three times every night
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 mawdu’ (fabricated) reports. Nothing concerning that has been proven from the Prophet (peace and blessings of Allah be upon him), so you should be careful and avoid that, and strive to follow the sahih Sunnah of the Prophet (peace and blessings of Allah be upon him), and shun that which is da’if (weak) and mawdu’ (fabricated). 
And Allah knows best.