Various solutions with respect to cross-slot scheduling for power saving in mobile communications are described. An apparatus receives, from a wireless network, a control signaling. According to the control signaling, the apparatus changes an aspect of a power profile of at least one bandwidth part (BWP) of a plurality of BWPs without causing data interruption regarding data transmission or reception by the apparatus. The apparatus also receives, from the wireless network, an indication. According to the indication, the apparatus adapts a new minimum applicable value of at least one of a downlink scheduling offset (K0), an uplink scheduling offset (K2), and an aperiodic channel state information reference signal (CSI-RS) triggering offset for an active DL BWP or an active UL BWP of the plurality of BWPs.