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.
It is desirable for a praying person to supplicate Allaah for the good of this world and the Hereafter before concluding the prayer (i.e. after he finishes the Tashahhud). It is most likely that the supplication at this time is answered as reported in authentic narrations.
As regards the supplication after concluding the prayer (after saying Salaam), if this is on a continuous basis and in congregation, then this is undoubtedly an innovation as this was neither reported from the Prophet nor from his companions . However, if a person individually supplicates after concluding the prayer, then this is not an innovation, rather this is something desirable according to the view of the majority of the scholars . It is reported in a Prophetic narration that the supplication is most likely to be answered in the last-third part of the night and after each obligatory prayer.