No. We don't have any authentic evidence that the Prophet Muhammad (SAWA) or any of his holy Progeny Ahlul Bayt (As) moved index finger during Tashahhud in prayers.
bismillāhi wa billāhi, assalāmu ʿalayka ayyuhan nabiyyu wa raḥmatullāhi wa barakātuh.
In the name of Allah and by Allah. Peace be upon you O Prophet, and Allah’s mercy and His blessings (be upon you too).
I also have a tutorial that could be of benefit as well:
If you realize during the Salah that you forgot to recite Tashahhud, your Salah is valid but you need to recite the Tashahhud immediately after Salah before saying any word.
If you realised that mistake after doing something else, your Salah is valid.
Tashahhud is obligatory but it is not Rokn. Rokn is the most important obligatory with out which Salah is invalid. Forgetting Tashahhud does not invalidate the Salah.
Tashahhud has obligatory part and recommended parts which can be added on the obligatory part. The obligatory part in Tashahhud is: ASHHADU ANLA ELAAHA ILLALLAH WAHDAHU LA SHAREEKA LAH WA ASHHADU ANNA MUHAMMADAN ABDOHU WA RASOOLUH ALLAHUMMA SALLI 'ALA MUHAMMAD WA AALI MUHAMMAD.
أشهد أن لا إله إلا الله وحده لا شريك له وأشهد أنّ محمدا عبده ورسوله اللهم صل على محمد وال محمد
The recommended parts are many e.g. BISMILLAH WA BILLAH WAL HAMDULILLAH WAL ASMAA'UL HUSNA LILLAH ASHHADU ANLA ELAAHA ILLAHLLAH WAHDAHU LA SHAREEKA LAH WA ASHHADU ANNA MUHAMMADAN 'ABDOHU WA RASOOLUH ALLAHUMMA SALLI 'ALA MUHAMMAD WA AALI MUHAMMAD WA TAQABBAL SHAFA'ATAHU WARFARIN DARAJATAH.
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