What immediately jumps to mind are the Qarmatians. As you point out (most) Muslim groups believe in some form of “al-Mahdi” who appears along with Jesus to usher in the end of days. Within Imami Shia belief this figure must be directly descended from the prophet Muhammad (through his daughter Fatima and her marriage to Ali).

The Qarmatians line of this descent is Ali to Hasan to Hussein to Zayn al-Abidin to Muhammad al-Baqir to Jafar al-Sadiq to Ismail ibn Jafar (included for simplicity) to finally Muhammad ibn Ismail. Upon al-Sadiq’s death Muhammad ibn Ismail fled the Hejaz and went into hiding, communicating with his followers through trusted missionaries and representatives (hujjas).

A little after 795 CE Muhammad ibn Ismail died. This fractured his supporters with a large amount refusing to believe he had died. To explain his absence, they began to preach that he had not died but gone into spiritual occultation and he would return as the Mahdi.

In Iraq this movement came under the control of Hamdan Qarmat during the 870s and he spread it rapidly. The Qarmatians reached their peak in the Qarmatian State in Bahrain founded in 899 CE by Abu Said al-Jannabi. However they were quickly weakened by a schism with what would become the Fatimids who claimed Abd Allah al-Mahdi (more on him and his claim to be the Mahdi later) was the rightful Imam and the great great grandson of the deceased (and not occulted) Muhammad ibn Ismail. In 902 the Qarmatian hostility towards Abd Allah forced his flight from Salamiyya to North Africa.

In 923 Abu Tahir al-Jannabi became leader of the Qarmatian State and they began to raid the Hajj caravans returning from Mecca. In 930 Abu Tahir headed an army that sacked Mecca and stole the black stone from the kaba.

In 931 Abu Tahir gave control of the Qarmatian State to a Persian man who he believed to be Muhammad ibn Ismail. In theory this was the triumphant return of al-Mahdi, where the believers would follow and set up a perfect nation before their final judgement. This was a disaster, this man began ritualistic cursing of Islamic prophets, anti-Arab sentiment and antinomianism. This shocked the rest of the Muslim world and had many within the Qarmatian State second guessing themselves. After about 80 days the apocalypse was off. “Muhammad ibn Ismail” had started to execute higher ups in the Qarmatian State and Abu Tahir admitted this man was not the Mahdi and had him killed.

Afterwards the Qarmatians returned to awaiting the return of Muhammad ibn Ismail with Abu Tahir claiming to represent him. They continued to raid pilgrimage routes and clash with the Abbasids and Fatimids. The Qarmatians gradually lost power as their population was won over by the Fatimid and possibly Ithna Ashari dawa (religious calling), as well as losing out militarily to the Abbasids. In 1077 the Qarmatian State was ended with the founding of the Uyunid dynasty.

As mentioned earlier Abd Allah al-Mahdi was a central figure in the schism between the Fatimids and the Qarmatians. He rent the communities when he claimed to be the rightful Imam of the time and that Muhammad ibn Ismail was 1. Dead and 2. Not the Mahdi.

Abd Allah wanted to establish a Shia Caliphate and leverage his role as the Mahdi to unify people under his rule. When the world continued after the establishment of his Caliphate the Fatimid conception of the Mahdi shifted. Instead of being somebody who brings about the end of times it became someone who brought about a new age for their community.

Sources:

Madelung W. (1959). Fatimiden und Bahrainqarmaten. Der Islam, 34.

Stern S. (1961). Isma’ilis and Qarmatians. L’Élaboration de L’Islam. Colloque de Strasbourg. Paris.

Halm H. (1996) Empire of the Mahdi: The Rise of the Fatimids. Handbook of Oriental Studies, the Near and Middle East. Vol 26. Leiden (trans. Michael Bonner)