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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The practice that you mentioned in the question is an innovation; neither the Prophet nor his companions have done so. Indeed the Prophet said: "Whoever performs an act that is not in accordance with ours (concerning religion), it will be rejected." [Al-Bukhari and Muslim] Another narration reads: "Whoever introduces into this faith of ours that which is not a part of it, it will be rejected." [Al-Bukhari and Muslim].
Therefore, gathering to read this specific verse a specified number of times and supplicate after finishing reading it, is an innovation in religion that must be stopped and whoever has done so must repent to Allaah from doing it.
Allaah knows best.