The Mughal Emperor who most significantly imposed Islamic Sharia law in his empire was Aurangzeb, who ruled the Mughal Empire from 1658 to 1707.

Aurangzeb was a devout Muslim and during his long reign, he took several steps to enforce Islamic law and orthodox religious practices throughout the Mughal territories. Some of his key actions included:

• He was imposing the Jizya tax on non-Muslims, which had been abolished by his predecessors.
• They are demolishing many Hindu temples and restricting the construction of new ones.
• They are enforcing the observance of Islamic rituals and practices, such as mandatory prayers and fasting.
• Appointing Islamic judges and theologians to oversee the implementation of Sharia law in the empire.
• Banning the sale and consumption of alcohol and other intoxicants.

Aurangzeb’s religious orthodoxy and efforts to impose Sharia were controversial even during his time, contributing to growing resentment among his non-Muslim subjects. This helped lead to increasing instability and the eventual decline of the Mughal Empire after his death. So in summary, Aurangzeb was the Mughal ruler who most aggressively tried to apply Islamic Sharia law across his domains.