“Friday Black,” a short-story collection that veers from absurd humor to extreme violence, is earning early raves and posing an inbox challenge for its debut author.

“I used to be on the outside, really, really, really wanting to be in,” said Nana Kwame Adjei-Brenyah, the 27-year-old writer whose book comes out on Tuesday. “Now I’m sort of on the inside, totally overwhelmed by emails.”

The...