With the advent of multicore platforms in designing Mixed-Criticality Systems (MCSs), simultaneous management of reliability and energy while guaranteeing an acceptable service level for low-criticality tasks is a crucial challenge. To ensure the reliability of the MCSs against transient faults, fault-tolerant techniques are employed which will increase energy consumption. To mitigate the energy overhead, the Dynamic Voltage and Frequency Scaling (DVFS) technique will be exploited. However, this technique might lead to violating the timing constraints of high-criticality tasks. Therefore, this paper presents, for the first time, the low-energy checkpointing technique to guarantee the reliability of multiple preemptive periodic mixed-criticality tasks in a multicore platform. In contrast to the previous works in checkpointing technique which consider a specific number of faults that all the tasks in the system should tolerate, in this paper, the number of tolerable faults for each execution section of a task, and in each voltage and frequency level is determined through proposed formulas to meet the reliability target based on safety standards. Then, our proposed method determines the number of checkpoints and their non-uniform intervals for the normal and overrun sections of each task to reduce energy consumption, respectively. Moreover, the unified demand bound function (DBF) analysis is proposed for analyzing the schedulability of the task set, where each high-criticality task meets its timing and reliability constraints, and low-criticality tasks execute based on their derived guaranteed periods in each operational mode of the system. Experimental results show that our proposed scheme meets the timing and reliability constraints while at the same time, improving the QoS of low-criticality tasks, and managing energy consumption with an average of 29.49%, and 32.78%, respectively.