We cannot write your assignment for you, but we can give you some help to get started. Diasporic writing refers to writing by members of culture groups who are dispersed - that is, not living in their native land. There is a large group, for example of Indian diasporic writerss (Sujata Bhatt, M.G. Vassanji, Salman Rushdie, etc.), a large group of African diasporic writers (Paule Marshall's, Jean Toomer, Ann Petry, etc.) - Asian diasporic writers, Jewish diasporic writers, Caribbean diasporic writers (Zee Edgell) and an ever-increasing pool of Eastern European diasporic writers (Aleksandar Hemon). Almost any people group living outside of their native land and writing (mostly these writers have a way of landing in the United States or Canada) are diasporic writers.
In order to answer your particular question, you will have to do some research on these writers to investigate what they write. You will find that the majority of them write about what they know - that is, their native land. Some of them write nostalgic works about their native land. They often express the idea that now that they are not living there, they can write objectively about the culture they left behind. For others, their themes center around the differences between their native lands and the land in which they are now living, the challenges of trying to adjust to the native land, the cluture clashes of old world vs new world, leaving the old ways behind, family, mores, etc. In their writing, they are often trying to find themselves, I have found. Most of the characters in their fiction are semi-autobiographical. Much of the fiction is "coming of age" in nature - i.e., what have they learned? In their writing, they are exploring the self and how the self relates to the culture, both old culture and new culture. So the diasporic writers write about community (new and old), but they concern themselves with how the self fits into the community.
There is some information about the African diasporic writers here on eNotes that might help you.