Currently, we rely on Internet of Things (IoT) for the betterment of our lifestyle which gives IoT an eloquent importance. It provides a deep vision for the digital world by embodying physical objects to the Internet. Along with the benefits it provides, it is also facing many challenges, especially from the security aspects. IoT infrastructure could be made flexible and cost effective by integrating Fog and Cloud computing technologies. However, these technologies are themselves associated with a number of security challenges. There are many cryptographic solutions proposed in the literature to secure IoT networks, but recent advances in Quantum Computing (QC) are a threat to these existing solutions. Predictions of exact arrival time in QC on a large scale cannot be made, but it raises threats by breaking the existing cryptographic solutions. So there is an urgency of Quantum-resistant solutions for securing IoT systems. In this paper, we present a model for securing the IoT framework in classical and Quantum world using post-Quantum cryptography and Artificial Intelligence (AI). In addition, we also implement and verify the working of the model on AVISPA tool.