CLOTH is a very vague word. It could be a piece of clothing, something to dry dishes with, something that you're going to make into a shirt . . . we don't really know. It would be a good idea to be more specific. As to the other question: In my opinion: Cloth with a rare design (the article A is needed) = Any kind of cloth (which may not be rare at all) that has a design on it which IS rare. Cloth of rare design. = A cloth which is manufactured in some way as to give it unusual features.

They are both unclear. Examples: I bought wash cloths having a rare design on them. I bought a towel with an interesting design on it. I bought a decorative towel with a unique design on it. I bought some cloth having an interesting pattern. ‘Of rare design’ could be ok but is wrong here. My grandfather had a clock of rare design. (It means that it works differently than most clocks)

Great question! Let’s break it down: 1. Which sentence is correct? Both sentences are grammatically correct: "I bought a cloth with rare design at the market." "I bought a cloth of rare design at the market." However, they have slightly different nuances and naturalness in usage.