The Mahdiyya Movement in Sudan overthrew the "Ottoman-Egyptian Regime in the early 1880s."
The Mahdiyya Movement was a religious and political movement that emerged in Sudan in the late 19th century. It was led by Muhammad Ahmad, who proclaimed himself the Mahdi or "guided one" and sought to overthrow the Ottoman-Egyptian regime that was ruling over Sudan at the time.
In 1881, the Mahdiyya Movement launched a successful uprising against the Ottoman-Egyptian forces, and in 1885, Muhammad Ahmad's forces captured and destroyed the city of Khartoum, killing its governor, British General Charles Gordon.
The Mahdiyya Movement then established a theocratic state in Sudan, which lasted until 1898 when it was defeated by British forces in the Battle of Omdurman.
Therefore, out of the given options, the correct answer is "Ottoman-Egyptian Regime in the early 1880s," as it was the regime that was overthrown by the Mahdiyya Movement in Sudan.