Born in Mombasa on 25th November 1936. Mulla Asgher is the eldest son of Mulla M.M. Jaffer of Mombasa. His grandfather Mulla Jaffer was a religious teacher in Zanzibar and Pangani.
Tracing the ancestry of Mulla Asgher. Maalim Najaf Tejani of Daressalaam has written: "Grandfather of Mulla Asgher was originally from Bhavnagar and migrated to Zanzibar in 1900. He died in Pangani in the Tanga region of Tanzania in 1918 and is buried there. He had gone to Pangani to teach Islamic education.
Father of Mulla Asgher was commonly well known as M.M. Jaffer or as Mulla Mohamed. After the demise of his father in 1918, M.M. Jaffer along with H.M. Rashid and Hassanali M. Kermali went to Lucknow in 1920 for religious education. They returned to Zanzibar in 1925. Upon their return, the three wanted to open a night school to impart Islamic education. Zanzibar Jamat did not permit them to do so as the Jamat was already running one such night school. With the assistance of Al Hajj Remtualla Alarakhia Tejani, they were however able to open such a School at a premises known as "Takim's Godown" owned by the Rashid Natha family.
In 1932, M.M. Jaffer migrated to Mombasa. In 1934, he married the only daughter of Mohamed Jaffer Sheriff Dewji. Mulla Asgher was born in 1936. M.M. Jaffer visited Zanzibar frequently to recite Majalis. He was very good at 'Nawha' recitations.