In the burgeoning field of the Internet of Things (IoT), ensuring secure and trustworthy communication between devices is paramount. This paper proposes a novel Trustworthy-Based Authentication Model (TBAM) integrated with Intrusion Detection Systems (IDS) leveraging deep learning algorithms to secure IoT-enabled networks. The proposed model addresses the dual challenges of authenticating legitimate devices and detecting malicious intrusions. Specifically, we employ a Convolutional Neural Network (CNN) to analyse network traffic patterns for intrusion detection, leveraging its prowess in feature extraction and classification. Additionally, a Long Short-Term Memory (LSTM) network is utilized for continuous monitoring and anomaly detection, capturing temporal dependencies in data flows that are indicative of potential security threats. The authentication mechanism integrates a trust evaluation system that assigns trust scores to devices based on their behaviour, enhancing the model's capability to distinguish between trusted and malicious entities. Our extensive experiments on real-world IoT datasets demonstrate that the TBAM significantly outperforms traditional security models in terms of detection accuracy, false-positive rate, and computational efficiency. Specifically, our model achieves a detection accuracy of 98.7%, a false-positive rate of 1.2%, and a processing time reduction of 30% compared to baseline models. This work contributes a robust, scalable, and efficient solution to the pressing security concerns in IoT networks, paving the way for more secure and reliable IoT applications.