Abstract: An acylsulfamide compound, or a pharmaceutically acceptable salt thereof, having NLRP3 inflammasome inhibitory activity, a pharmaceutical composition comprising the same, and their medical use, etc., are provided. A compound of Formula [Ia]: or a pharmaceutically acceptable salt thereof, wherein a partial structure: is: Ring Cy is an optionally substituted heteroaryl or phenyl; RDy and REy are each independently hydrogen, optionally substituted C1-6 alkyl, optionally substituted C1-4 haloalkyl, optionally substituted C3-6 cycloalkyl, optionally substituted heterocycloalkyl, or optionally substituted heteroaryl, or alternatively, RDy and REy may combine together with the nitrogen atom to which they attach to form heterocycloalkyl, etc.