This paper concentrates on the controller synthesis problem for load frequency control (LFC) of multi-area power systems under resilient event-triggering communication scheme (RETCS) and periodic denial-of-service (DoS) jamming attacks. Firstly, a periodic RETCS under the given DoS attacks is designed, which can eliminate impact of the periodic DoS jamming attacks effectively. Second, a state error dependent switched LFC model for multi-area power systems is given. Then, a co-design method for RETCS and LFC gains is developed. Finally, the effectiveness of the proposed method is demonstrated by a two-area power system.