There is immense virtue in the fast of Mi'raj day. Sheikh Jilani (﵀) has dedicated a chapter in his famous book, Ghunyat, solely to discuss this.

فصل: في فضل صيام يوم السابع والعشرين من رجب[عبد القادر الجيلاني، الغنية لطالبي طريق الحق، ٣٣٢/١]

Chapter discussing the virtue of the fast observed on Rajab 27 - (Al-Ghunyat - 1/332)

Then he (﵀) narrates:

من صام يوم السابع والعشرين من رجب كتب له ثواب صيام ستين شهرًا، [عبد القادر الجيلاني ,الغنية لطالبي طريق الحق ,1/332]

If one fasts and makes blessed the day of the twenty-seventh of Rajab, Allah will record for him the reward of sixty years of worship. (Ghunyat: 1/332)

This Hadith from Abu Hurairah (﵁) is narrated by Hujjat al-Islam Imam Abu Hamid al-Ghazali (﵀), the Mujaddid (reformer) of the fifth Hijri century, in his Ihya', stating that the fast of Rajab 27 is Sunnah. "The fast of the twenty-seventh of Rajab is equivalent to the fast of sixty months." (Ihya' 1/361).

Imam Ibn Hajar al-Haytami (﵀) says:

قيل: ومن البدع: صوم رجب، وليس كذلك، بل هو سنةٌ فاضلةٌ، كما بينتُه في «الفتاوى» وبسطت الكلام فيه. ( فتح المبين بشرح الأربعين - ١/٢٢٦)

It has been said by some that the fast of Rajab is a Bid'ah. That is not correct. Rather, it is a very meritorious Sunnah. I have discussed this extensively in the Fatawa. (Fath al-Mubin - 1/226)

It can be seen in his Fatawa that a complaint was brought to Ibn Hajar al-Haytami (﵀) that some scholar was forbidding people from fasting on that day, saying that the Hadiths about the fast of the month of Rajab are Da'if (weak). The great scholar [Ibn Hajar] replied:

وأمّا اسْتِمْرارُ هَذا الفَقِيهِ عَلى نَهْيِ النّاسِ عَنْ صَوْمِ رَجَب فَهُوَ جَهْلٌ مِنهُ وجُزافٌ عَلى هَذِهِ الشَّرِيعَةِ المُطَهَّرَةِ فَإنْ لَمْ يَرْجِع عَنْ ذَلِكَ وإلّا وجَبَ عَلى حُكّامِ الشَّرِيعَةِ المُطَهَّرَةِ زَجْرُهُ وتَعْزِيرُهُ التَّعْزِيرَ البَلِيغَ المانِعَ لَهُ

If the scholar you mentioned persists in this claim and prevents people from fasting in this month, it is merely his lack of knowledge. It is also carelessness concerning the pure Shari'ah of this Din. If he does not retract from this claim, it is obligatory for the Hakim (ruler) who implements the Shari'ah to deter him from it and take action against him.

Ibn Hajar (﵀) further says:

والذي يَنْهى عَنْ صَوْمِهِ جاهِلٌ مَعْرُوفٌ بِالجَهْلِ ولا يَحِلُّ لِمُسْلِمٍ أنْ يُقَلِّدَهُ (فتاوي الكبرى الفقهية -٢/٥٤)

Those who oppose the fast of Rajab are foolish. Known as utterly foolish. It is not permissible for any Muslim to follow them! (Fatawa al-Kubra - 2/54)

Many other jurisprudential Imams have clarified that fasting on the very day of Mi'raj is Sunnah.

Allama Sulaiman al-Jamal (﵀) records:

Fasting on the day of Mi'raj is Sunnah. (Hashiyat al-Jamal: 3/468)

ويستحب صوم يوم المعراج [حاشيةالجمل٣/٤٦٨]

Moreover, all Fuqaha' (jurists) have taught that fasting on the 27th, 28th, and 29th of every Arabic month is Sunnah. In that respect, it is clear that fasting on the twenty-seventh day of Rajab is Sunnah.

Now, Ibn Hajar (﵀) also responds to those who deny the fast by saying the Hadith is Da'if (weak). It is a matter of Ijma' (consensus) in the Din that virtuous deeds can be performed based on Da'if Hadiths. Even Ibn Taymiyyah, the leader of the innovators, admits this.

Ibn Hajar al-Asqalani (﵀), whom the innovators quote to say these Hadiths are Da'if, openly states this matter in the same book.

" اشتهر أن أهل العلم يتسامحون في إيراد الأحاديث في الفضائل وإن كان فيها ضعف، ما لم تكن موضوعة" (تبيين العجب بما ورد في فضل رجب (23-26 )

It is well-known among people of knowledge that there is leniency in using Da'if Hadiths for virtuous deeds.

Therefore, we must be wary of such obstructors of goodness...

For more references:

روى أبو هريرة أن رسول الله ﷺ قال من صام يوم سبع وعشرين من رجب كتب الله له صيام ستين شهرًا (٣) وهو اليوم الذي أهبط الله فيه جبرائيل عليه السلام على محمد ﷺ بالرسالة.[أبو حامد الغزالي ,إحياء علوم الدين ,1/361]
وليلة النصف منه وليلة سبع وعشرين منه وهي ليلة المعراج [أبو حامد الغزالي ,إحياء علوم الدين ,1/361]
قيل: ومن البدع صوم رجب، وليس كذلك بل هو سنة فاضلة، كما بينته في الفتاوي وبسطت الكلام عليه. [البكري الدمياطي ,إعانة الطالبين على حل ألفاظ فتح المعين ,1/313]
إعانة الطالبين على حل ألفاظ فتح المعين ١/‏٣١٣