The statement sadaq Allaahul ‘Adheem after ending recitation of the Quraan is a bid’a (innovation) because the Prophet sal Allaahu alaiyhi wa sallam did not do it, nor the Rightly Guided Caliphs, nor the rest of the Companions radiy Allaahu ‘anhum – nor the scholars of the salaf rahimahumallaah – despite their abundance in reciting the Quraan, and their carefulness and their knowledge of its greatness.
So saying this (statement) and adhering to it at the end of the recitation is a newly invented innovation, and indeed it is established from the Prophet sal Allaahu alaiyhi wa sallam that he said:
Whoever brings something new into this affair of ours which is not from it, then it will be rejected. Reported by Bukhaari and Muslim.
And he said: Whoever does an action which is not from our affair then it will be rejected. Reported by Muslim.
And with Allaah is the tawfeeq. And may peace and blessings be upon our Prophet Muhammad and his family and his Companions.