Methods and apparatuses for downlink data buffering considering cross carrier scheduling in a wireless communication system. The UE receives configuration of a first serving cell and a second serving cell from a network and receives and/or monitors a first PDCCH transmitted on the second serving cell, wherein the first PDCCH schedules a first PDSCH. The UE receives and/or monitors a second PDCCH transmitted on the second serving cell, receives and/or buffers the second PDSCH based on a first TCI state used for PDCCH quasi co-location indication of a CORESET, and receives and/or buffers the first PDSCH based on a second TCI state.