To what extent are the rumors true about the appearance of a grandson of the Prophet Muhammad, peace and blessings be upon him, and can he have grandsons despite the death of all his sons and the sons of his daughters?

The direct children of the Prophet, peace and blessings be upon him, all passed away. However, his distant, indirect descendants are still present, and the Mahdi will be from among these descendants. It has been narrated in a hadith (definition): "The Mahdi is from my 'Itrah (family), from the children of Fatima." And also: "The world will not pass away, or the world will not come to an end, until a man from my household, whose name matches my name, rules the Arabs." The exact time of the Mahdi's appearance is unknown, and what people mention about his imminent appearance is mere conjecture with no evidence to support it.