Final answer:
Imam Jafar al-Sadiq had the longest Imamat period, serving for about 34 years. He is part of the direct lineage from Ali in Shia Islam, which is considered the legitimate succession of leadership.
Step-by-step explanation:
The Imam with the longest Imamat period among the options provided is Imam Jafar al-Sadiq. He was the sixth Imam in Shia Islam and served as the spiritual leader for about 34 years from 765 to 799 CE. Shia Muslims consider the succession of Imams to be a direct lineage stemming from Ali, the cousin and son-in-law of Muhammad, the prophet of Islam.
Shia beliefs state that the legitime caliphs should be direct descendants of Ali through his marriage to Fatima, the daughter of Muhammad. This lineage is referred to in Shia Islam as the Ahl al-Bayt, the 'People of the House,' pertaining to the household of Muhammad. Therefore, among the listed Imams, Imam Jafar al-Sadiq had the longest period of leading the community. He is recognized for his contributions to Muslim scholarship, including his teachings on jurisprudence and theology.