All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The Sunnah does not report any tradition on performing acts of worship specially on New Hijri Year’s Eve, and a Muslim must beware of any innovation in religion. The Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever introduces something into our religion which does not belong to it, it will be rejected." In another narration, he, sallallaahu ‘alayhi wa sallam, said: "Whoever does an act which does not belong to our religion, it is to be rejected." [Al-Bukhari and Muslim]
Scholars defined a religious innovation as any act of worship that the Prophet, sallallaahu ‘alayhi wa sallam, did not do while there was the possibility and a need for doing it with no impediment preventing him, sallallaahu ‘alayhi wa sallam, from performing it. Also, the prohibition from performing acts of worship specially on Friday night was reported. It was narrated on the authority of Abu Hurayrah that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Do not perform special voluntary prayers on the night of Friday." [Muslim] Since this prohibition to perform special voluntary prayers on a specific night, whose excellence over the other nights is established, it would with even greater reason be prohibited to perform special voluntary prayers on other nights that have no virtue established.
Moreover, an attachment to New Year Eve pertains to the traditions of the unbelievers and we are commanded not to imitate them. Thus, this is prohibited based on that reason, too. There is no harm in inviting Muslims to perform voluntary prayers at night in congregation if the purpose is worshipping, teaching people how to perform it and making them accustomed to it. However, if they do this only for the purpose of congregation believing that it would be more virtuous and better than any other occasions, the invitation will be impermissible for the reason mentioned above.
Allaah Knows best.