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The structure of blood vessels in the retina is a crucial factor in identifying and forecasting various eye diseases like cardiovascular diseases, diabetes, and other diseases. Therefore, detecting the structure of blood vessels from retinal fundus images is a critical field of research in healthcare. This study employed a novel deep learning model to segment vessels for different diseases, including Glaucoma, Diabetic Retinopathy (DR), and Age-related Macular Degeneration (AMD). We considered multiple transfer learning-based models and discovered that the ResNet-based U-Net architecture was the most effective for vessel segmentation, achieving the highest Dice Score above 84% for disease-agnostic, and 82%-84% for disease-specific conditions. We believe the proposed methodology will help to advance retinal vessel segmentation process and enhance the screening process of diseases based on retinal fundus images in clinical settings of Qatar Biobank as well as other biobanks across the globe. © 2023 IEEE.