Reference: Fataawa ash-Shaykh al-‘Allaamah Muhammad Naasiruddeen al-Albaanee fil-Madeenah wal-Imaaraat – Page 95-96
Question: What is the manner [in which] the [index] finger should be moved during the prayer in tashahhud?
Response: There is the hadeeth of Waa.il ibn Hajar [wherein it mentions] he saw the Prophet (sal-Allaahu ‘alayhi wa sallam) when he was sitting in tashahhud in prayer, and he said: And I saw him moving his finger and supplicating [as he was moving] it.
This movement does not mean [simply] raising and lowering [the finger], since no hadeeth exists to suggest this; Rather, that which is intended by the moving [of the finger] is moving it [whilst it is extended from the resting clenched hand] in its place.
And it has been authentically reported from Imaam Ahmad, that he said: “And it is to be moved vigorously.”
 Transmitted by Ahmad 4/318, Abu Daawood 726-728, an-Nasaa.ee 2/127 and Ibn Maajah 810.