Anas, may Allaah be pleased with thim, reports that it was the practice of our beloved Prophet, sallallaahu ‘alayhi wa sallam, after the prayer to place his right hand on his forehead (and in some narrations on his head) and recite the following supplication: "In the name of Allaah. None is worthy of worship but Allah, The Most Merciful, The Ever Merciful. O Allaah! Relieve my distress and sadness". What is the level of authenticity of the above-mentioned hadith?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

The hadeeth in reference was cited by a number of scholars with very weak chains of narration.

At-Tabarani narrated it on the authority of Sallaam At-Taweel, who narrated it on the authority of Zayd Al-‘Ammiyy, who narrated on the authority of Mu‘aawiyah ibn Qurrah that Anas ibn Maalik, may Allah be pleased with him, said, “After prayer, the Prophet, sallallahu ‘alayhi wa sallam, used to wipe his forehead with his right hand and say, ‘Bismillah allathi laa ilaaha illa huwa Ar-Rahmaan-ur-Raheem. Allahumma ath-hib ‘anni al-Hamma wal-Hazan.’ (Which means: In the name of Allah. None is worthy of worship but Allah, The Most Merciful, The Ever Merciful. O Allah! Relieve my distress and sadness.)” At-Tabaraani commented on the hadeeth, saying, “Zayd was the only reporter who narrated this report on the authority of Mu‘aawiyah, and Sallaam was the only reporter narrating it (on the authority of Zayd).”

The narrations of Sallaam At-Taweel were rejected by Hadeeth scholars and he was accused of lying. His teacher was Zayd Al-‘Ammiyy (Ibn Al-Hawaari) who was also classified as a weak reporter according to the majority of Hadeeth scholars.

The hadeeth was also cited by Abu Nu‘aym with a chain of narration containing Daawood ibn Al-Muhabbar, who was declared a liar. Therefore, Al-Albaani classified this hadeeth as Mawdhoo’ (fabricated) in As-Silsilah Adh-Dha‘eefah: 1059.

Abu Nu‘aym cited it in his book Tareekh Baghdad, and its chain of narration included Katheer ibn Sulaym, who was declared a weak reporter by the consensus of Hadeeth scholars. An-Nasaa'i and others described him as Matrook (discarded; known for lying).

Allah knows best.