Methods and apparatuses for physical downlink control channel (PDCCH) enhancements in a wireless communication system. A method of operating a user equipment (UE) includes receiving a synchronization signals and physical broadcast channel (SS/PBCH) block and determining a set of configurations for a control resource set (CORESET #0) for a Type0-PDCCH. The set of configurations include a subcarrier spacing (SCS) for the CORESET #0 that is same as the SS/PBCH block; a multiplexing pattern between the CORESET #0 and the SS/PBCH block; a time domain offset (O) to determine slots including monitor occasions for the Type0-PDCCH; and an index of a starting symbol within at least one of the slots. For a first multiplexing pattern between the CORESET #0 and the SS/PBCH block, the time domain offset (O) is configurable based on the SCS of the CORSET #0. The method further includes receiving the Type0-PDCCH based on the set of configurations for CORESET #0.