Alauddin Khalji besieged and took the fort of Chittor in 1303. That much is not in question: Amir Khusrau, a poet at his court, accompanied the campaign and described it in the Khazain ul-Futuh within a few years.
The story attached to the siege is that the sultan came for Padmini, queen of Chittor, having seen her reflection; that the fort held out; and that when it fell she led the women and children into a fire rather than be taken. The collective self-immolation is jauhar, and jauhar as a practice is well documented in Rajput history. It is not the same thing as sati. Sati followed the death of a husband and was performed by a widow; jauhar was performed by women and children collectively in the face of a fort about to fall, alongside the men riding out to die. Conflating the two, which is common in popular writing, loses what each was.
Khusrau does not mention Padmini. Neither does any other contemporary or near-contemporary chronicler of the campaign. The narrative first appears in the Padmavat, an Awadhi poem composed by the Sufi poet Malik Muhammad Jayasi in 1540, more than two centuries after the siege, and composed as an allegory rather than as a chronicle.
Jauhar itself is not in doubt. Rajput chronicle and Persian chronicle both record collective immolations at falling forts, and the practice has its own logic, distinct from anything to do with widowhood: it belonged to the last hours of a siege, alongside saka, the ride out of the gate by men who did not expect to return. Chittor is traditionally credited with three of them, in 1303, 1535 and 1568, and the later two rest on much firmer ground than the first.