The first determination is whether the book is fiction or non-fiction. Since the story is not a recount of actual events with actual people, it is fiction.
Does the story include elements of magic, mythical beasts, or anything that is absolutely impossible? No, then it is not fantasy.
Does the story include elements of advanced technology that does not exist yet, but may be possible in the future? No, then it is not Science Fiction.
Is the story set during a specific era in the past? No, then it is not Historical fiction.
Could the plot actually happen in real-life? Yes, that makes this Contemporary Realistic Fiction.
The genre is that of the historical novel. Curtis sets his tale of civil war strife in Alabama circa 1963 (as indicated in the title) and follows the travails of ten year old Kenny Watson and his African American family (which includes his Momma and Dad, sister Joetta and brother Byron.) The family travels from the relatively non-racist Flynt, Michigan, to the seat of the country's civil rights struggles, Birmingham, Alabama.
Just FYI...this novel won multiple awards, including a Newbery Honor and the Coretta Scott King Honor for best novels of the year (1995) for young adults.