Is Salat al-Raghaib Sunnah?
Question

Is Salat al-Raghaib Sunnah and is it mustahabb to offer this prayer?
Praise be to Allah.What is Salat al-Raghaib?
Salat al-Raghaib is one of the innovations (bid`ahs) that have been introduced in the month of Rajab. It is done on the night of the first Friday in Rajab , between Maghrib and `Isha, and is preceded by fasting on the first Thursday of Rajab. 
When was Salat al-Raghaib first introduced?
Salat al-Raghaib was first introduced in Bayt al-Maqdis (Jerusalem) in 480 AH. There is no report that the Prophet (peace and blessings of Allah be upon him) did it, or any of his Companions, or any of the best generations or imams. This alone is sufficient to prove that it is a reprehensible innovation, and it is not a praiseworthy Sunnah. 
Scholarly views on Salat al-Raghaib
The scholars have warned against it and pointed out that it is innovation and misguidance. 

Al-Nawawi (may Allah have mercy on him) said in al-Majmu’ (3/548) 

The prayer which is known as Salat al-Raghaib, which is twelve rak’ahs that are offered between Maghrib and ‘Isha on the night of the first Friday in Rajab, and praying one hundred rak’ahs on the night of Nisf Sha’ban (halfway through Sha’ban) are both reprehensible innovations. No one should be deceived by the fact that they are mentioned in Qut al-Qulub and Ihya ‘Ulum al-Din, or by the hadith which is quoted in these two books, because all of that is false. No one should be deceived by some of those imams who were confused about the ruling on these prayers and wrote essays stating that they are mustahabb, for they are mistaken in that. Imam Abu Muhammad ‘Abd al-Rahman ibn Isma’il al-Maqdisi wrote a valuable book showing that they are false, and he did well in that, may Allah have mercy on him.”

Al-Nawawi also said in Sharh Muslim: 

“May Allah curse the one who fabricated and introduced that, for it is a reprehensible innovation, one of the innovations which constitute misguidance and ignorance, and it involves obvious evils. A number of imams have written valuable works explaining that those who offer this prayer and the one who invented it are misguided, and they quoted a great deal of evidence to show that it is wrong and false, and that those who do it are misguided.”

Ibn ‘Abidin said in his Hashiyah (2/26): 

“It says in al-Bahr: Hence we know that it is makruh to gather for Salat al-Raghaib, which is done on the first Friday of Rajab, and that it is an innovation. 
The scholar Nur al-Din al-Maqdisi wrote a good essay on this topic which he called Rad’ al-Raghib ‘an Salat al-Raghaib, in which he covered most of the comments of earlier and later scholars among the four madhhabs.”

Ibn Hajr al-Haytami (may Allah have mercy on him) was asked: Is it permissible to offer Salat al-Raghaib in congregation or not? 

He replied: 
“Salat al-Raghaib is like the prayer that is known as laylat al-nusf min Sha’ban (half way through Sha’ban). These are two reprehensible innovations and the hadith which speaks of them is mawdu’ (fabricated). It is forbidden to offer these prayers either individually or in congregation.” Al-Fatawa al-Fiqhiyyah al-Kubra, 1/216 

Ibn al-Haj al-Maliki said in al-Madkhal (1/294): 

“Among the innovations that have been introduced in this noble month (i.e., Rajab) is that on the night of the first Friday thereof, they pray Salat al-Raghaib in the mosques, and they gather in some mosques and do this innovation openly in the mosques with an imam and congregation, as if it is a prescribed prayer… the view of Imam Malik (may Allah have mercy on him) is that it is makruh to do this prayer, because it was not done by those who came before, and all goodness is to be found in following them (may Allah be pleased with them).”

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

“As for innovating a prayer which is done regularly with a certain number of rak’ahs, with a certain recitation and at a certain time in congregation, like these prayers that are being asked about here – such as Salat al-Raghaib on the first Friday of Rajab, and halfway through Sha’ban, and the night of the twenty-seventh of Rajab, and so on – these are not prescribed in Islam, according to the consensus of the imams of Islam, as was stated by the reliable scholars. No one established such a thing but those who are ignorant and innovators. Things like this open the door to changing the laws  and rituals of Islam and becoming like those who instituted things which Allah has not ordained.” (Al-Fatawa al-Kubra, 2/239) 

Shaykh al-Islam was also asked about it and he said: 

“This prayer was not offered by the Messenger of Allah (peace and blessings of Allah be upon him) or by any of the Sahabah or the Tabi’in or the imams of the Muslims. The Messenger of Allah (peace and blessings of Allah be upon him) did not enjoin it and neither did any of the salaf or imams. They did not suggest that this night has any virtue for which it should be singled out. The hadith which is narrated concerning that from the Prophet (peace and blessings of Allah be upon him) is false and fabricated, according to scholarly consensus. Hence the scholars said that it is forbidden and not mustahabb.” (Al-Fatawa al-Kubra, 2/262) 

It says in al-Mawsu’ah al-Fiqhiyyah (22/262): 

“The Hanafis and Shafi’is stated that praying Salat al-Raghaib on the first Friday of Rajab, or on Laylat al-nusf min Sha’ban, in a specific manner or with a specific number of rak’ahs, is a reprehensible innovation. 
Abu’l-Faraj ibn al-Jawzi said: Salat al-Raghaib is a fabrication that is falsely attributed to the Messenger of Allah (peace and blessings of Allah be upon him). They stated that these prayers are a bid’ah and are forbidden for a number of reasons. There is no report from the Sahabah, Tabi'in or imams about these two prayers. If they were prescribed in Islam then the salaf would not have been unaware of them. Rather they were introduced in the 400s (fifth century AH).”
For more about the month of Rajab, see these answers: 75394 , 317278 , 92780 , 332295 , 114424 , and 171509 .
And Allah knows best.