Was Ali ibn Abi Talib (may Allah be pleased with him) exiled from Medina during the time of Uthman ibn Affan (may Allah be pleased with him), and what is the extent of the authenticity of this exile and its reasons?

Ali ibn Abi Talib (may Allah be pleased with him) was in Medina throughout the entirety of Uthman's (may Allah be pleased with him) caliphate. He did not move to Kufa until his own caliphate. What the questioner has alluded to is a lie and a fabrication.