Part of a fancy bedding set

I believe the answer is:

sham

(Other definitions for sham that I've seen before include "Feign" , "'Fake, pseudo (4)'" , "Mash, being counterfeit" , "Phoney, bogus" , "Bogus hams" .)

I've seen this clue in The New York Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.