It depends on the circumstances and the sect.
If we are talking religiously, the terms used are: Caliph, Mullah, Sheikh, Ayatollah (Shiites Only), etc.
If we are talking politically, the terms used are: Sultan, King, Emir, etc.
I think the term you are looking for is caliphate, and the ruler was called a caliph.
The Muslim ruler, Akbar, mandated religious and cultural toleration.
Muslim Ruler.
Chief or ruler of a Narragansett territory
sultans
Muslim Ruler.
Humayun
The easternmost city in Muslim territory is Jayapura, the current name of the country in which it is located is Indonesia.
Mali has had numerous Muslim leaders. Perhaps the most famous was Mansa Musa, who was a ruler of Mali during the 1300s. He embarked on a holy trip to the Muslim city of Mecca in 1324.
Emir - Title of a Muslim (Mostly Arabic) ruler.
Because their ruler wanted to convert Ghana's ruler to a Muslim.
Mohammad Ghori