In a new era of medical imaging, deep-learning models have emerged to identify and diagnose Temporomandibular Joint Osteoarthritis (TMJ-OA) from panoramic X-ray scans. The Convolutional Neural Network (CNN) with U-Net models attain better efficiency to segment and classify TMJ-OA over the past years. But the efficiency of deep-learning models primarily depends on the hyperparameters. Also, the TMJ-OA detection is not satisfactory because of an improper segmentation of the mandibular condyle and glenoid fossae on X-ray scans. To solve these problems, this article develops a Tri-Stage Deep-Learning Model (TSDLM) for TMJ-OA identification and diagnosis. This model aims to accurately segment mandibular condyles and glenoid fossae on X-ray scans using a 3D U-Net. In this model, the initial two stages adopt the 3D U-Net model for Region-Of-Interest (ROI) extraction and mandibular condyle region segmentation. In the third stage, the ResNet50 model is utilized to learn the features from the segmented areas and classify the TMJ-OA for accurate diagnosis. Besides, a Reptile Search Algorithm (RSA) is proposed for hyperparameter optimization, which enhances mandibular condyle segmentation and TMJ-OA identification. Finally, the experimental results exhibit that the TSDLM reaches an accuracy of 92.29% on the panoramic dental X-ray image dataset compared to the conventional deep-learning models.