Glaucoma is the second most common cause of blindness. A glaucoma suspect has risk factors that increase the possibility of developing glaucoma. Evaluating a patient with suspected glaucoma is challenging. The "donut method" was developed in this study as an augmentation technique for obtaining high-quality fundus images for training ConvNeXt-Small model. Fundus images from GlauCUTU-DATA, labelled by randomizing at least 3 well-trained ophthalmologists (4 well-trained ophthalmologists in case of no majority agreement) with a unanimous agreement (3/3) and majority agreement (2/3), were used in the experiment. The experimental results from the proposed method showed the training model with the "donut method" increased the sensitivity of glaucoma suspects from 52.94% to 70.59% for the 3/3 data and increased the sensitivity of glaucoma suspects from 37.78% to 42.22% for the 2/3 data. This method enhanced the efficacy of classifying glaucoma suspects in both equalizing sensitivity and specificity sufficiently. Furthermore, three well-trained ophthalmologists agreed that the GradCAM++ heatmaps obtained from the training model using the proposed method highlighted the clinical criteria.Clinical relevance- The donut method for augmentation fundus images focuses on the optic nerve head region for enhancing efficacy of glaucoma suspect screening, and uses Grad-CAM++ to highlight the clinical criteria.