What is the ruling on raising the hands in supplication after the prescribed prayers, following the tasbeeh, and should the one who does so be condemned, and is this a matter of scholarly disagreement?

Supplicating after obligatory prayers is prescribed, as it is established from the Prophet, peace be upon him, in numerous authentic hadiths. Imam Al-Bukhari even dedicated a chapter to it. Many authentic hadiths indicate supplication after prayer, such as the hadith (definition) of Mu'adh ibn Jabal: "O Mu'adh, by Allah, I love you, so do not abandon saying after every prayer: 'O Allah, help me to remember You, to thank You, and to worship You in the best manner.'" Also, the hadiths of Zayd ibn Arqam and Suhayb.

Furthermore, raising the hands during supplication is also prescribed. Many authentic hadiths from the Prophet, peace be upon him, confirm this, such as the hadith of Abu Musa Al-Ash'ari: "The Prophet, peace be upon him, called for water, performed ablution, then raised his hands and said: 'O Allah, forgive Ubayd Abi Amir,' until I saw the whiteness of his armpits." And the hadith of Ibn 'Umar concerning the story of Khalid, and the hadith of Abu Hurayrah: "O Allah, guide Daws," and the hadith of Jabir regarding the man who emigrated with him: "The Prophet, peace be upon him, said: 'O Allah, forgive his two hands,' and he raised his hands." And the hadith of 'Aisha: "She saw the Prophet, peace be upon him, supplicating with his hands raised, saying: 'O Allah, I am but a human being,'" and many others.

In conclusion, both supplication and raising hands after prayer are prescribed, and there is no harm in consistently performing them. However, it is disliked for someone whom the common people emulate to consistently perform some Sunnah (definition) acts, lest the common people mistake them for obligatory duties.