All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If you dedicate the night of Friday every week for Tahajjud (night optional prayers), then you have to stop such a deed for the Prophetic Hadeeth reported by Muslim from Abu Hurayrah 'Do not single out the night of Friday with prayer or good deed from among other nights and do not favor Friday with fasting from among other days unless you are accustomed to fast (or do good deeds) on the same day (or night) [such as a person fasting every other day]”
In case you assign any other night, for example Sunday or another day, then there is a difference of opinion among the scholars on this issue.
Abu al-‘Abbaas ar-Ramli said: “One may infer that it is not disliked to specify some night (save Friday), and this is correct.”
Al-Azru'i said: “We can not give a decisive opinion in this concern since it is possible to be a form of innovation.” But, according to the approved (reliable) opinion of Imam ash-Shaafi'i, it is not disliked, although it is better and safer not to do such a deed on a regular basis since many scholars believe that it is an innovation.
Ibn Al-'Arabi said: “As recorded by Ibn Hajar al-Haythami : “Apparently, singling out any night or day with some form of worship constitutes an innovation since we are ordered to avoid doing that on the day or night (of Friday).”
In brief, it is not disliked to spend some night in Tahajjud prayer, but not as a habit.
As for the prayer of ar-Raghaa-ib, it is a prayer of 12 Rak'ahs offered between the Magrib and ‘Isha prayers on the first Friday of Rajab. In fact, it is an innovation as stated by the scholars of Islam.
Therefore, there is no similarity between this prayer and singling out the Friday night for prayers.
So, you are to stick to the Sunnah as stated above.
For more benefit, please refer to Fatwa 87228.
Allah knows best.