Literally “wool broadcloth,” a çuka or çuha was an overcoat made of, yes, wool broadcloth. Wool broadcloth was a top-quality fabric whose cost could rival that of many silks, a mainstay of any gentleman’s or lady’s wardrobe (as well as the winter wear of any less well-to-do person who could afford it), so a çuka was a garment of no small prestige.
We don’t have a description of how a çuka was cut. It may have been a generic term for any overcoat made of wool broadcloth. However, given the sheer number of men in Ottoman art who wear full-length wool overcoats with hanging sleeves, the absence of any known term for these coats, and the omnipresence of çuka in well-to-do people’s wardrobes, I suspect çuka was the term for the robe with hanging sleeves when it was made of wool broadcloth.
In the painting of a gentleman’s son (c. 1625), his black overcoat with hanging sleeves is probably a çuka .