Hadith: When the Messenger of Allah (may Allah's peace and blessings be upon him) sat for supplication, he would put his right hand on his right thigh and his left hand on his left thigh, point with his index finger, place his thumb on his middle finger, and cover his knee with the palm of his left hand

عن عبد الله بن الزُّبير رضي الله عنهما قال: «كان رسول الله صلى الله عليه وسلم إذا قَعد يَدْعُو، وضع يَده اليُمْنَى على فخِذِه اليُمْنَى، ويَده اليُسْرَى على فخِذِه اليُسْرَى، وأشَار بِإِصْبَعِهِ السَّبَّابَة، ووضَع إبْهَامَه على إِصْبَعِهِ الوُسْطَى، ويُلْقِم كَفَّه الْيُسْرَى رُكْبَتَه».
[صحيح] - [رواه مسلم]

‘Abdullāh ibn Az-Zubayr (may Allah be pleased with him) reported: When the Messenger of Allah (may Allah's peace and blessings be upon him) sat for supplication, he would put his right hand on his right thigh and his left hand on his left thigh, point with his index finger, place his thumb on his middle finger, and cover his knee with the palm of his left hand.
[Authentic hadith] - [Narrated by Muslim]

Explanation

This Hadīth describes what the Prophet used to do in his Tashahhud, which he calls a ''supplication.'' When he took that position, Ibn ‘Umar says: “The Prophet would put his left hand on his left knee” [Muslim]. The Tashahhud is to say: "Greetings, prayers, and good words be to Allah. Peace be upon you, O Prophet, and the mercy and blessings of Allah. Peace be upon us and the righteous slaves of Allah..." It is called a ''supplication'', due to these two invocations: "peace be upon you" and "peace be upon us.'' When the Prophet sat for Tashahhud, he would put his right hand on his right thigh and his left hand on his left thigh. In doing so, he would prevent himself from making unnecessary movements with his hand. Putting the hand on the thigh means that the fingertips will reach the knee. In the narration from Wā'il ibn Hujr: ''The Prophet put his left palm on his left thigh and knee, and put the edge of his right elbow on his right thigh" [An-Nasā'i]. So by putting the edge of the elbow on the thigh, the tips of one's fingers will definitely reach the knee. An-Nawawi said: "Scholars are agreed that it is recommended to put the hand on the knee. Some say that the fingers should be bent over the knee to cover it.'' This position applies in both the first and the second Tashahhud. The Prophet would point with his index finger to indicate the Oneness of Allah. This is an act of the Sunnah to observe from the start to the end of the Tashahhud. ‘Abdullāh ibn ‘Umar said: "When the Messenger of Allah (may Allah's peace and blessings be upon him) sat for the Tashahhud, he would put his left hand on his left knee and his right hand on his right knee, form a zero shape, and point with his index finger." [Muslim] Also, Wā'il ibn Hujr said: "Then the Prophet sat and put his left leg under him, put his left hand on his left thigh and the edge of his right elbow on his right thigh. Then he held two of his fingers and made a circle, and I saw him make a circle with his thumb and middle finger, and point with his index finger" [Abu Dawūd]. One points with the index finger to indicate the Oneness of Allah, Most High, thereby demonstrating the belief and words with an action. Ibn ‘Umar said: "Indeed, (the index finger) is more painful to the devil than being beaten with an iron rod." [Ahmad]. Pointing with the index finger does not necessarily mean moving it. Finally, does covering one's knees with one's palm indicate either holding the knees or not? Ibn ‘Umar said: "When the Prophet (may Allah's peace and blessings be upon him) sat in prayer, he put his two hands on his two knees...and his left hand stretched over his knee." So these are two options that conform with the Sunnah and it is recommend to observe them alternately.