Hudhayfah (may Allah be pleased with him) narrated that,” Whenever the the Prophet (peace and blessings be upon him) read a verse about Allah’s punishment , he would seek refuge in Allah. And whenever He read a verse mentioning Allah’s mercy , he would ask Allah for His mercy. Hudhayfah said, “ Whenever the Prophet (peace and blessings be upon him) bowed he would say, “ Subhana Rabbil Atheem.” and when He prostrated He’d say,” Subhana Rabbil ‘Ala.”.

Collected by Ahmed 6/ 24 , Abu Dawud 873, and others. Graded as being Hasan by Al-Albani

Benefits for this topic:

Shaykh Abdul Azeez bin Baz (may Allah have mercy on him) said:

It’s Sunnah for every muslim who reads the Quran during prayer or elsewhere to ask Allah for His bounty at the verses of mercy. And when the Muslim reads a verse mentioning Allah’s punishment, he seeks refuge from the Hell-fire. Furthermore when a Muslim reads an ayah that deems Allah above something he declares it. He declares it by saying, “ Subhanahu wa Ta’ala.”

It’s recommended for every Muslim who reads : Is not Allah the Best of judges? [At-tin 8] to say ,” Indeed! : I believe that to be true.” Moreover when he reads, “ Is not He (Allah Who does that), Able to give life to the dead? (Yes! He is Able to do all things).[ Al-Qiyamah 40], he says, “ Indeed!: I bear witness to this.” The servant should say, “ I believe in Allah.” when he reads ,” Then in what statement after this (the Qur'an) will they believe? [ Al-Mursaalat 50].

After the slave recites the verse, “ Then which of the Blessings of your Lord will you both (jinns and men) deny? [ Ar-Rahman 13] He says, “ We don’t deny any verses from our Lord. And after reading ,” Glorify the Name of your Lord, the Most High,”[Al-A’la 1], he says,” Subhana Rabbil ‘Ala”

All of these acts are recommended for the Imam, followers , and individual reciting the Quran. These words are dua, and dua is wanted from the Muslim. This resembles the saying, “ Ameen” after Fatihah: and Ameen should be said in prayer and elsewhere after Fatiha.

Majmu’ Fataawa Bin Baz vol 26 page 62-63