Praise be to Allah, and may peace and blessings be upon the Messenger of Allah. To proceed:
First: The Emergence of the Mahdi
It has been established that the Mahdi will appear at the end of time, and that his appearance will occur before the emergence of the Dajjal and before the descent of Jesus, peace be upon him. However, no authentic text has established the specific time of his appearance.
Likewise, there is no explicit authentic hadith specifying the place from which he will emerge. There are reports connecting him to Khurasan or the East, and others claiming that he will emerge from Makkah or from another place, but these reports have not been established as authentic.
Among these is the hadith concerning the Black Banners, which hadith scholars have classified as weak. Likewise, the report claiming that he will emerge from a village in Yemen called “Kur‘ah” is extremely weak. Its chain of transmission includes ‘Abd al-Wahhab ibn al-Dahhak, who was abandoned as a narrator of hadith.
Therefore, it is not correct to definitively state a specific place for the emergence of the Mahdi, because no authentic text establishing this has been proven.
Second: The Descent of Jesus, Peace Be Upon Him
As for Jesus, son of Mary, peace be upon him, it is authentically established in Sahih Muslim that he will descend at the white minaret east of Damascus.
The Prophet ﷺ said in the hadith of al-Nawwas ibn Sam‘an رضي الله عنه, describing his descent:
“He will descend at the white minaret east of Damascus.”
Then he will pursue the Dajjal until he catches up with him at the gate of Ludd and kills him.
The scholars have affirmed that the descent of Jesus, peace be upon him, at this location is authentically established, and that he will kill the Dajjal, break the cross, and kill the swine, as stated in the authentic hadiths.
Conclusion:
There is no authentic text establishing a specific place from which the Mahdi will emerge. What is established is that he will appear at the end of time before the descent of Jesus, peace be upon him. As for Jesus, peace be upon him, it is authentically established that he will descend at the white minaret east of Damascus.
And Allah knows best.