In an example from the perspective of a first User Equipment (UE), in response to performing successful listen before talk (LBT), the first UE determines a channel occupancy time (COT). The first UE determines whether or not a second sidelink transmission, to be performed by a second UE, is within the COT. The first UE determines information, associated with LBT type and/or cyclic prefix (CP) extension, for inclusion in a first sidelink transmission in the COT, wherein whether the information includes first information associated with LBT type and/or CP extension or the information includes second information associated with LBT type and/or CP extension is based on the determination of whether or not the second sidelink transmission is within the COT. The UE transmits, to the second UE, the first sidelink transmission in the COT. The first sidelink transmission includes the information. The second sidelink transmission is associated with the first sidelink transmission.