Traditions are available from every infallible about the presence and the existence of Imam Mahdi (as). These context of traditions extend beyond just his birth and include aspects regarding his reappearance, his occultation and even cover the events after his reappearance. Here are some traditions.
Hazrat Fatemah Zahra (sa)
Hazrat Zahra (sa) told Imam Husayn (as),
When you were born Holy Prophet (sawa) came to me, took you in his arms and said, O Fatemah! Take your Husayn and know that he is the father of nine Imams (as) and the infallible Imams (as) will be born from his progeny, the ninth of whom will be the Qaem. (Isbat al-Huda volume 2 page 552)
Three more traditions in this regard have been narrated from her (as)
Imam Hasan (as)
Imam (as) said, The number of Imams (as) after the Holy Prophet (sawa) are twelve, of which nine will be from the progeny of my brother Husayn (as) and the Mahdi of the nation will also be from among them. (Isbat al-Huda volume 2 page 555)
Four more traditions in this context have been narrated from him (as).
Imam Husayn (as)
Imam (as) said, Twelve Imams are from us. The first is Ali ibne Abi Talib (as) and the last will be my ninth son, and he is Qaem with the truth. Allah, The Blessed and the High, through his Holy existence will give life to the dead earth and the true religion will be victorious over all other religions, even if the polytheists are averse. The Mahdi will be away from the eyes of the people for a period of time. During his occultation, a group of people will deviate, while others will remain steadfast, due to which they will be involved in fear, afflictions and grief. They will be taunted with questions like – If your belief is true, when will your promised Imam reappear? But know that whoever during the period of occultation will bear the torments and false accusations about him (as) he is like the person who has accompanied the Holy Prophet (sawa) in battle. (Beharul Anwar volume 51 page 133, Isbat al-Huda at volume 2 pages 333, 399)
Thirteen more traditions in this regard have been narrated from him (as)
Imam Sajjad (as)
Imam (as) prophesied, The birth of our Qaem will be hidden from the people in such a way that people will say that he is not yet born. The reason behind his hidden birth is that when he will begin his revolution there will not be anyone’s allegiance (bayat) upon him. (Beharul Anwar volume 51 page 135)
Ten more traditions in this regard have been narrated from him (as)
Imam Mohammed Baqir (as)
Imam (as) said to Abaan ibne Taghlib (ra), I swear by Allah, Imamate is that position which has reached us from the Holy Prophet (sawa). After the Holy Prophet (sawa) the Imams (as) are twelve in number of which nine are from the progeny of Imam Husayn (as). Mahdi will be from us and he will protect the religion in the last days. (Isbat al-Huda volume 2 page 559)
Sixty-two more similar traditions in this regard have been narrated from him (as)
Imam Jafar Sadiq (as)
He (as) said, The person who believes in all the Imams (as) but denies the existence of Imam Mahdi (as) is like the one who believes in all the past Prophets (as) but denies the Prophethood of Hazrat Mohammed Mustafa (s.a.w.a.). He (as) was asked, From whose progeny will Mahdi arise? He (as) replied, He will be the fifth son of the seventh Imam (Imam Musa Kazim (as)). But he will be concealed and it is not permitted for you to take his name. (Beharul Anwar volume 51 page 143; Isbat al-Huda at volume 6 page 404)
One hundred and twenty three more traditions in this regard have been narrated from him (as)
On the basis of these traditions some of the past scholars do not permit to take Imam’s (as) name and instead say M-H-M-D.
Imam Musa Kazim (as)
In his reply to the question of Yunus bin Abdur Rahman – Are you Qaem? Imam (as) replied, Yes I am Qaem with the truth, but that Qaem who will free the earth from Allah’s enemies and fill the earth with justice and equality is my fifth son. Since he will fear for his life, he will be in long occultation. In occultation, a group of people will deviate from religion. But some others will remain firm in their belief. Then Imam (as) said, What should I say about the Shiahs who during the occultation will withhold our Wilayat and will be firm on our friendship and will bear enmity with our enemies. They are from us and we are from them. They are satisfied with our Imamat and we will be pleased with them. Then what can I say about them? By Allah, in Paradise they will enjoy our grades. (Beharul Anwar volume 51 page 115; Isbat al-Huda at volume 6 page 417)
Five more traditions in this context have been narrated from him (as).
Imam Ali Reza (as)
In reply to the question of Rayyan ibne Salt, are you Sahebul Amr (Master of the Affair / Master of the Time)? Imam (as) said, Yes I am Sahebul Amr, but not that Sahebul Amr who will fill the earth with justice and equity. The promised Qaem is he who will look like a youth even in old age, when he will reappear and he will be so powerful that if he extends his hand towards the largest tree, he will uproot it. If he shouts from between the mountains, the hardest of rocks will crumble to pieces. He will have the staff of Hazrat Musa (as) and the ring of Hazrat Sulayman (as). He will be my fourth son. When Allah the Almighty will wish, he will disappear from the eyes of the people. Then Allah will make him reappear and through him He will fill the earth with justice and equality like it would be filled with injustice and inequality. (Beharul Anwar volume 52 page 322; Isbat al-Huda volume 6 page 419)
Eighteen more similar traditions have been narrated from him (as)
Imam Mohammed Taqi (as)
Imam (as) disclosed to Abdul Azim Hasani, Our Qaem is that promised Mahdi whose intezar (awaiting) will be obligatory during his occultation and his obedience will be obligatory during his reappearance. He will be my third son. I swear by Allah who sent Muhammad (sawa) as a Prophet and selected us for Imamate, even if one day is left for the world to end, Allah will prolong it so much that the Mahdi will reappear. He will fill the earth with justice and equality like it will be filled with injustice and oppression. Allah will change his affair (reappearance) in one night, just like He transformed the affair of His Prophet – Hazrat Musa (as) in one night. Hazrat Musa (as) had gone to get some firewood for his wife and returned with the position of Prophethood. Then Imam (as) declared, Awaiting for the reappearance is the best action of our Shiahs. (Beharul Anwar volume 51 page 151; Isbat al-Huda at volume 6 page 420)
Five more traditions in this regard have been narrated from him (as)
Imam Ali Naqi (as)
He (as) said, After me, my son Hasan will be Imam and after Hasan his son Qaem will be Imam whose justice will encompass the entire world. (Isbat al-Huda at volume 6 page 275)
Five more similar traditions have been narrated from him (as)
Read More: 40 Traditions from Ahle Bayt (as) about Imam Mahdi (as)