The Indian Muslim who sat on the throne of Delhi during the Sultanate period was Nasiruddin Khusrau Shah. He was the only Indian Muslim to become the Sultan of Delhi during this period.

Background:
The Sultanate period in India began in 1206 when Qutub-ud-din Aibak established the Slave dynasty. This period saw the rise of various Muslim dynasties in India, which ruled over the northern and central parts of the country. The Sultanate period lasted till 1526 when Babur, the founder of the Mughal Empire, defeated Ibrahim Lodi in the Battle of Panipat.

Nasiruddin Khusrau Shah:
Nasiruddin Khusrau Shah was the ruler of the Khilji dynasty, which ruled over Delhi from 1290 to 1320. He came to the throne in 1320 after the death of his father, Alauddin Khilji. Nasiruddin was not the rightful heir to the throne, but he managed to seize power with the help of his mother and other supporters.

Achievements:
During his reign, Nasiruddin Khusrau Shah focused on strengthening the administration and improving the economy of Delhi. He introduced several reforms, such as reducing taxes and increasing the salaries of government officials. He also patronized scholars and poets, and his court was known for its cultural and intellectual vibrancy.

Challenges:
Despite his achievements, Nasiruddin Khusrau Shah faced several challenges during his reign. He had to deal with rebellions from his own family members, who were unhappy with his accession to the throne. He also faced threats from neighboring kingdoms, particularly from the Mongols, who invaded Delhi during his reign.

Legacy:
Nasiruddin Khusrau Shah's reign was short-lived, but he left a lasting impact on Delhi's history. He was the only Indian Muslim to become the Sultan of Delhi during the Sultanate period, and his reign was marked by cultural and intellectual achievements. His reforms and policies laid the foundation for the subsequent rulers of Delhi, who continued to build on his legacy.