Wireless sensor networks (WSNs) have been vastly employed in the collection and transmission of data via wireless networks. This type of network is nowadays used in many applications for surveillance activities in various environments due to its low cost and easy communications. In these networks, the sensors use a limited power source which after its depletion, since it is non-renewable, network lifetime ends. Due to the weaknesses in sensor nodes, they are vulnerable to many threats. One notable attack threating WSN is Denial of Sleep (DoS). DoS attacks denotes the loss of energy in these sensors by keeping the nodes from going into sleep and energy-saving mode. In this paper, the Abnormal Sensor Detection Accuracy (ASDA-RSA) method is utilised to counteract DoS attacks to reducing the amount of energy consumed. The ASDA-RSA schema in this paper consists of two phases to enhancement security in the WSNs. In the first phase, a clustering approach based on energy and distance is used to select the proper cluster head and in the second phase, the RSA cryptography algorithm and interlock protocol are used here along with an authentication method, to prevent DoS attacks. Moreover, ASDA-RSA method is evaluated here via extensive simulations carried out in NS-2. The simulation results indicate that the WSN network performance metrics are improved in terms of average throughput, Packet Delivery Ratio (PDR), network lifetime, detection ratio, and average residual energy.