It was narrated that 'Abdullah said:"When we sat during the prayer with the Messenger of Allah (ﷺ), we used to say: 'Peace (salam) be upon Allah(SWT), peace be upon so-and-so and so-and-so.' The Messenger of Allah (ﷺ) said: 'Do not say peace (salam) be upon Allah (SWT), for Allah (SWT) is As-Salam (the Source of peace; the One free from all faults). Rather say: At-tahiyyatu lillahi wasalawatu wat-tayibaat, as-salamu 'alaika ayah-Nabiyyu wa rahmatAllahi wa baraktuhu. As-salamu 'alaina a 'ala ibad illahis-salihin (All compliments, prayers and pure words are due to Allah. Peace be upon you O Prophet, and the mercy of Allah and His blessings. Peace be upon us and upon the righteous slaves of Allah.) If you say that, it will be for every righteous slave in the heavens and on earth, "ashadu an la ilaha ill Allah, wa ashhadu anna Muhammadan 'abduhu wa rasuluhu (I bear witness that that none has the right to be worshipped except Allah, and I bear witness that Muhammad is His slave and messenger.) Then let him choose any supplication that he likes to say after that.'"
أَخْبَرَنَا يَعْقُوبُ بْنُ إِبْرَاهِيمَ الدَّوْرَقِيُّ، وَعَمْرُو بْنُ عَلِيٍّ، - وَاللَّفْظُ لَهُ - قَالاَ حَدَّثَنَا يَحْيَى، قَالَ حَدَّثَنَا سُلَيْمَانُ الأَعْمَشُ، قَالَ حَدَّثَنِي شَقِيقٌ، عَنْ عَبْدِ اللَّهِ، قَالَ كُنَّا إِذَا جَلَسْنَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم فِي الصَّلاَةِ قُلْنَا السَّلاَمُ عَلَى اللَّهِ مِنْ عِبَادِهِ السَّلاَمُ عَلَى فُلاَنٍ وَفُلاَنٍ . فَقَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم " لاَ تَقُولُوا السَّلاَمُ عَلَى اللَّهِ فَإِنَّ اللَّهَ هُوَ السَّلاَمُ وَلَكِنْ إِذَا جَلَسَ أَحَدُكُمْ فَلْيَقُلِ التَّحِيَّاتُ لِلَّهِ وَالصَّلَوَاتُ وَالطَّيِّبَاتُ السَّلاَمُ عَلَيْكَ أَيُّهَا النَّبِيُّ وَرَحْمَةُ اللَّهِ وَبَرَكَاتُهُ السَّلاَمُ عَلَيْنَا وَعَلَى عِبَادِ اللَّهِ الصَّالِحِينَ فَإِنَّكُمْ إِذَا قُلْتُمْ ذَلِكَ أَصَابَتْ كُلَّ عَبْدٍ صَالِحٍ فِي السَّمَاءِ وَالأَرْضِ أَشْهَدُ أَنْ لاَ إِلَهَ إِلاَّ اللَّهُ وَأَشْهَدُ أَنَّ مُحَمَّدًا عَبْدُهُ وَرَسُولُهُ ثُمَّ لْيَتَخَيَّرْ مِنَ الدُّعَاءِ بَعْدُ أَعْجَبَهُ إِلَيْهِ يَدْعُو بِهِ " .
Nesai
The Book of Forgetfulness (In Prayer) • Hadith 1298