The Internet of Things (IoT) is considered the future of the Internet due to its immense potential. It has captured the interest of researchers who are exploring new possibilities in this field. Unlike the current internet structure, IoT involves the connection of billions of devices and entails a significant exchange of data, diverse traffic, and resource availability. The increasing use of IoT devices in vulnerable environments has presented two major challenges for researchers: authenticating sensor nodes and ensuring secure data routing. These challenges become more difficult by the presence of wireless sensors in communication devices, where all devices are not authenticated or have up-to-date software. Among the various IoT attacks, the Sybil attack poses a significant threat to the network. Consequently, the conventional solutions used for conventional wireless networks do not apply to wireless sensor networks due to the differences in algorithms and associated costs in terms of processing and power consumption. To address these challenges, an extended signed response-based (ESRES) solution is proposed. The proposed framework utilizes a pre-distributed key embedded in a sensor node, while the authentication process employs a dual key-based algorithm with linear complexity. In this mechanism, the node uses pre-distributed keys to respond to a random challenge number sent by the server or sink, thus proving its legitimacy. Since there are different types of IoT networks, such as hierarchical and centralized structures, the proposed authentication scheme is designed to be flexible and implementable for both types. The performance of the proposed framework is analyzed and evaluated, considering the probability of attack detection with different authentication key pool sizes for different parameters i.e., processing overhead, probability, and power consumption.