Imam as-Suyuti (d. 911 H.), may Allah have mercy upon him, mentioned in his book Adhkaar ul-Adhkaar (pg. 23),

“If he passes a verse of mercy, he asks Allah for it. If he passes a verse of punishment, he seeks refuge in Allah from it If he passes a verse transcending Allah from any deficiency, then he glorifies Him”. End.

It is authentic. The proof for this is the following Hadith of Hudhayfah (may Allah be pleased with him),

إِذَا مَرَّ بِآيَةٍ فِيهَا تَسْبِيحٌ سَبَّحَ وَإِذَا مَرَّ بِسُؤَالٍ سَأَلَ وَإِذَا مَرَّ بِتَعَوُّذٍ تَعَوَّذَ

” And when he recited the verses which referred to the Glory of Allah, he glorified (by saying Subhan Allah-Glory to my Lord the Great), and when he recited the verses which tell (how the Lord) is to be begged, he (the Holy Prophet) would then beg (from Him), and when he recited the verses dealing with protection from the Lord” [Muslim no. 72]

“After reciting,

‘Is not He (Allah Who does that), Able to give life to the dead? (Yes! He is Able to do all things) [75:40]’

he should say, “Of course I bear witness to that”. End.

It is authentic. The proof for that is,

كَانَ رَجُلٌ يُصَلِّي فَوْقَ بَيْتِهِ وَكَانَ إِذَا قَرَأَ ‏{‏ أَلَيْسَ ذَلِكَ بِقَادِرٍ عَلَى أَنْ يُحْيِيَ الْمَوْتَى ‏}‏ قَالَ سُبْحَانَكَ فَبَلَى فَسَأَلُوهُ عَنْ ذَلِكَ فَقَالَ سَمِعْتُهُ مِنْ رَسُولِ اللَّهِ صلى الله عليه وسلم

A man used to pray on the roof of his house. When he recited the verse, “Is not He able to bring the dead to life?” [Surah al-Qiyamah:42] he would say, ‘Glory be to You, then, why not?’ They asked him about it, and he replied, ‘I heard it from the Messenger of Allah (ﷺ)'” [Saheeh Sunan Abi Dawood no. 884]

“After reciting,

‘Glorify the Name of your Lord, the Most High” [87:1]

he should say: “Glory be my Lord the Most High”. End.

It is authentic. The proof for that is the following,

عَنِ ابْنِ عَبَّاسٍ، أَنَّ النَّبِيَّ صلى الله عليه وسلم كَانَ إِذَا قَرَأَ ‏{‏ سَبِّحِ اسْمَ رَبِّكَ الأَعْلَى ‏}‏ قَالَ ‏”‏ سُبْحَانَ رَبِّيَ الأَعْلَى ‏”‏ ‏
Ibn ‘Abbas reported when the prophet (ﷺ) recited, “Glorify be the Name of your Lord, the Most High” He would say, ”Glorify be My Lord the Most High” [Saheeh Sunan Abi Dawood no. 883]

Note: Shaikh al-Albani (d. 1420 H.), may Allah have mercy upon him, said,

“What is apparent is that the recommendation for this is for everyone who is praying/leading prayer except the one being lead in prayer. For if he says,

“Glorify be My Lord the Most High”

then it would busy him from being silent which was commanded to be in the statement of the Exalted,

“So, when the Quran is recited, listen to it, and be silent that you may receive mercy [7:204]”

And Allah knows best”. End. [Asl Sifatus-Salah (pg. 408)]

“After reciting

‘Then in what statement after this (the Quran) will they believe’ [77:50]

he should say, ‘We believe in Allah.’ And after reciting,

‘Is not Allah the Best of judges?’ (95: 8)

he should say, ‘Certainly, and I am one of those who testify to that.'”. End.

These two are not authentic. They are based on the following Hadith:

سَمِعْتُ أَبَا هُرَيْرَةَ، يَقُولُ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏”‏ مَنْ قَرَأَ مِنْكُمْ ‏{‏ وَالتِّينِ وَالزَّيْتُونِ ‏}‏ فَانْتَهَى إِلَى آخِرِهَا ‏{‏ أَلَيْسَ اللَّهُ بِأَحْكَمِ الْحَاكِمِينَ ‏}‏ فَلْيَقُلْ بَلَى وَأَنَا عَلَى ذَلِكَ مِنَ الشَّاهِدِينَ وَمَنْ قَرَأَ ‏{‏ لاَ أُقْسِمُ بِيَوْمِ الْقِيَامَةِ ‏}‏ فَانْتَهَى إِلَى ‏{‏ أَلَيْسَ ذَلِكَ بِقَادِرٍ عَلَى أَنْ يُحْيِيَ الْمَوْتَى ‏}‏ فَلْيَقُلْ بَلَى وَمَنْ قَرَأَ ‏{‏ وَالْمُرْسَلاَتِ ‏}‏ فَبَلَغَ ‏{‏ فَبِأَىِّ حَدِيثٍ بَعْدَهُ يُؤْمِنُونَ ‏}‏ فَلْيَقُلْ آمَنَّا بِاللَّهِ ‏”‏
Abu Hurayrah: The Messenger of Allah (ﷺ) said: When one of you recites “By the fig and the olive” (Surah 95) and comes to its end “Is not Allah the best judge?” (verse 8), he should say: “Certainly, and I am one of those who testify to that.” When one recites “I swear by the Day of Resurrection” (Surah 75) and comes to “Is not that one able to raise the dead to life? (verse 40), he should say: “Certainly.” And when one recites “By those that are sent” (Surah 77), and comes to “Then in what message after that will they believe? ” (Surah 50), he should say: “We believe in Allah.” [Daif Abi Dawood (no. 887)]

“After reciting,

‘So which of the favors of your Lord would you deny?’ [Surah ar-Rahman]

then he says, ‘We do not deny any of Your favors our Lord! And Yours is praise.'”. End.

The scholars differed on this. It is reported in Tirmidhi and others,

عَنْ جَابِرٍ، رضى الله عنه قَالَ خَرَجَ رَسُولُ اللَّهِ صلى الله عليه وسلم عَلَى أَصْحَابِهِ فَقَرَأَ عَلَيْهِمْ سُورَةَ الرَّحْمَنِ مِنْ أَوَّلِهَا إِلَى آخِرِهَا فَسَكَتُوا فَقَالَ ‏ “‏ لَقَدْ قَرَأْتُهَا عَلَى الْجِنِّ لَيْلَةَ الْجِنِّ فَكَانُوا أَحْسَنَ مَرْدُودًا مِنْكُمْ كُنْتُ كُلَّمَا أَتَيْتُ عَلَى قَوْلِهِِ ‏:‏ ‏(‏ فبأَىِّ آلاَءِ رَبِّكُمَا تُكَذِّبَانِ ‏)‏ قَالُوا لاَ بِشَيْءٍ مِنْ نِعَمِكَ رَبَّنَا نُكَذِّبُ فَلَكَ الْحَمْدُ ‏”
Jabir (may Allah be pleased with him) said: “The Messenger of Allah (ﷺ) came out to his Companions, and recited Surat Ar-Rahman from its beginning to its end for them, and they were silent. So he said: ‘I recited it to the Jinns on the ‘Night of the Jinns,’ and they had a better response to it than you did. Each time I came to Allah’s saying: ‘Which of your Lords favor do you deny.’ They said: “We do not deny any of Your favors our Lord! And Yours is praise.”

Shaikh al-Albani graded it Hasan in Saheeh at-Tirimidhi (no. 3291) however it was graded weak by Ibn ul-‘Uthaymeen [Tafseer al-Hujurat to Hadid (pg. 307)] and Shaikh Muqbil bin Haadi al-Waadi’ee in Ahaadith al-Mu’allah (pg. 86)]

“After reciting,

‘Say (O Muhammad):,’Tell me! If (all) your water were to be sunk away, who then can supply you with flowing (spring) water?’ [67:30]

he says, “All praise is due to Allah”.

There is no proof for this.

Shaikh Bin Baz (d. 1420 H.), may Allah have mercy upon him, said,

“Nothing authentic has come in relation to “Tell me! If (all) your water were to be sunk away, who then can supply you with flowing (spring) water”. We do not know of anything reported. Some people mention some Ahaadith but we do not know of them having any origin”. End. [al-Fa’waid al-‘Ilmiyyah min ad-Duroos al-Baaziyyah (2/499)]

And Allah knows best

Faisal bin Abdul Qaadir bin Hassan
Abu Sulayman