Aga Khan is the hereditary title

Hereditary Title

Hereditary titles, in a general sense, are titles, positions or styles that are hereditary and thus tend or are bound to remain in particular families....

 of the Imam

Imam

An imam is an Islamic leadership position, often the worship leader of a mosque and the Muslim community. Similar to spiritual leaders, the imam is the one who leads Islamic worship services. More often, the community turns to the mosque imam if they have a religious question...

 of the largest branch of the Ismā'īlī

Ismaili

' is a branch of Shia Islam. It is the second largest branch of Shia Islam, after the Twelvers...

 followers of the Shī‘a faith. They affirm the Imamat

Imamah (Shi'a Ismaili doctrine)

The Ismaili view on the Imamah differs from the Twelver Shi'a view, in particular because the Imam in Ismailism is the Noor of God . Ismailis believe that the Noor of God is present in the Imam, and that there is only a Ẓāhirī difference between each one...

 of the descendants of Ismail ibn Jafar, eldest son of Imam Ja'far al-Sadiq

Ja'far al-Sadiq

Jaʿfar ibn Muhammad al-Sādiq was a descendant of Muhammad and a prominent Muslim jurist. He is revered as an Imam by the adherents of Shi'a Islam and as a renowned Islamic scholar and personality by Sunni Muslims. The Shi'a Muslims consider him to be the sixth Imam or leader and spiritual...

, while the larger Twelver branch of Shi`ism follows Ismail's younger brother Musa al-Kazim and his descendants.

Abdullah Jafar bin Muhammad As-Sadiq's sons, Ismail bin Jaffar and Abul Hassan Musa bin Jaffar, are followed by Twelver Shiites.