The answer is: In this prostration, one says: “Glory be to my Lord, the Most High,” because when Allah’s statement was revealed,

“Glorify the Name of your Lord, the Most High,” [Surah al-A‘la]

—the Prophet, may Allah bless him and grant him peace, said: “Say it in your prostration.” (1) This includes both prostration in the prayer and the prostration of recitation. He should also say: “Glory be to You, O Allah, our Lord, and all praise is Yours. O Allah, forgive me,” for two proofs:

The first proof is Allah’s statement:

“Only those believe in Our verses who, when they are reminded of them, fall down in prostration and glorify the praises of their Lord.” [Surah al-Sajdah: 15]

This is a verse of prostration.

The second proof is the hadith of Aishah, may Allah be pleased with her: “The Messenger of Allah, may Allah bless him and grant him peace, would often say while bowing and prostrating: ‘Glory be to You, O Allah, our Lord, and all praise is Yours. O Allah, forgive me.’” (2)

There is also a hadith reported by some of the compilers of the Sunan: “O Allah, for You I have prostrated; in You I have believed; and upon You I have relied. My face has prostrated to Allah, who created it, fashioned it, and brought forth its hearing and sight by His power and might. Blessed is Allah, the best of creators.” (3) “O Allah, record for me through it a reward, remove from me through it a sin, make it a treasure for me with You, and accept it from me as You accepted it from Your servant David.” (4)

If he says this, it is good. And if he adds further supplication, there is nothing wrong with that.