The question asks about the literary school (المدرسة الأدبية) that emerged in the diaspora (المهجر). In Arabic literary history, المهجر refers to the Arab emigrant communities, particularly those who settled in the Americas in the late 19th and early 20th centuries.
The literary movement that arose among these emigrant Arab writers is known as الرابطة القلمية (the Pen League). It was founded in New York in 1920 by prominent writers including Gibran Khalil Gibran (جبران خليل جبران), who served as its president, and Mikhail Naimy (ميخائيل نعيمة), who served as its advisor. The Pen League sought to break free from the rigid classical conventions of Arabic literature, embracing themes of spirituality, nature, nostalgia for the homeland, and individual freedom.
The other options represent different literary movements: المدرسة الرومانسية (the Romantic School) is a broader movement not specific to the diaspora; مدرسة الديوان (the Diwan School) was founded by Abbas Mahmoud al-Aqqad, Ibrahim al-Mazini, and Abd al-Rahman Shukri in Egypt; and المدرسة الواقعية (the Realist School) is a general literary approach focused on depicting everyday life. None of these is specifically associated with المهجر.