Is it permissible to act upon the narration "He moves it, supplicates with it" – which is considered an anomalous and weak narration due to its addition of something not found in 11 other narrations – because it conforms to the practice of the people of Medina, and is that valid and legislated?

None of the scholars have explicitly stated that moving the finger during the tashahhud is a practice of the people of Medina in toto. Rather, what is mentioned in the books of the Malikis is that it is a practice of some of the shaykhs. Maliki jurists have differed regarding its movement, and the adopted position (madhhab) among the Malikis is to move it, contrary to Ibn al-Arabi, who prohibits it. If it were established that the practice of the people of Medina was to move it, that would be another preponderant factor supporting the narration of moving it. Scholars have differed regarding the authenticity of the narration "he moves it" (yuḥarrikuhā); some have authenticated it, while others have ruled it shādh (aberrant). The matter in this regard is broad.