The medieval Indian literary work `Darbar-i-Akbari` was written by Muhammad Hussain.

Option 1, Muhammad Hussain, is the correct answer.

Option 2, Malik Muhammad Jayasi, is incorrect. Malik Muhammad Jayasi is known for writing the famous epic poem "Padmavat," which narrates the legend of Rani Padmini.

Option 3, Abul Fazl, is incorrect. While Abul Fazl was a prominent figure in Akbar`s court and the author of the famous historical work "Akbar-nama," he did not write `Darbar-i-Akbari.`

Option 4, Amir Khusrau, is incorrect. Amir Khusrau was a renowned poet during the medieval period in India and wrote numerous works. However, `Darbar-i-Akbari` is not one of his compositions.

Therefore, option 1, Muhammad Hussain, is the correct answer. However, it is important to note that the option does not provide further information about the identity or background of Muhammad Hussain.