The Shi’ite denomination of Islam is found mostly in Iran, Persia and partly in Iraq. Adherents represent about 10-15% of today’s Muslims.¹
Historically speaking, the Shi’ites and Sunnis split over a disagreement about the legitimacy of Mohammad’s successors (Caliphs)—not entirely unlike the Protestant refusal to recognize the authority of the Catholic Papacy.
¹ I was never a huge fan of demographics and religion, preferring the experiential and doctrinal aspects of faith. So rather than rewrite what Wikipedia presents so well, I’ll simply copy and paste:
The demographic breakdown between the two denominations is difficult to assess and varies by source, but a good approximation is that 85-90% of the world’s Muslims are Sunni and 10-15% are Shia, with most Shias belonging to the Twelver tradition and the rest divided between many other groups. Sunnis are a majority in most Muslim communities: in Southeast Asia, China, South Asia, Africa, and most of the Arab world. Shia make up the majority of the citizen population in Iraq, Iran, Azerbaijan, and Bahrain, as well as being a politically significant minority in Lebanon. Azerbaijan is predominantly Shia; however, practicing adherents are much fewer. Indonesia has the largest number of Sunni Muslims, while Iran has the largest number of Shia Muslims (Twelver) in the world. Pakistan has the second-largest Sunni as well as the second-largest Shia Muslim (Twelver) population in the world. » https://en.wikipedia.org/wiki/Shia%E2%80%93Sunni_relations