(a) It is reported from Sayyiduna Ali (may Allah be pleased with him) that when he sat for the tashahhud he would say 'Bismillah' (In the name of Allah).
(b) In another narration, reported from al-Harith (may Allah have mercy on him), when Sayyiduna Ali (may Allah be pleased with him) was in the tashahhud he would say: 'Bismillahi wa billah' (In the name of Allah and with Allah).
(c) There is also a connected (mawsul) narration from Urwah (may Allah have mercy on him), but it does not mention 'Bismillah' (In the name of Allah).
(d) It is reported from Sayyiduna Ibn Umar and Sayyidah Aishah (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) used to say 'Bismillah' (In the name of Allah) before the tashahhud.
(e) It is reported from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that he heard a man reciting: 'Bismillah, at-tahiyyat' (In the name of Allah, all verbal acts of worship), and Sayyiduna Ibn Abbas (may Allah be pleased with them both) rebuked him.
A narrator like al-Harith is not used as evidence. The authentic narration from Sayyidah Aishah (may Allah be pleased with her) does not mention 'Bismillah', except in what Muhammad bin Ishaq bin Yasar alone narrated. Thabit bin Zuhayr (who narrated it from Ibn Umar and Aishah from the Prophet) is munkar al-hadith (his narrations are rejected) and da'if (weak), and what is authentic from Ibn Umar is that it is mawquf (his own practice).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2834