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Drug targets are the main focus of drug discovery due to their key role in disease pathogenesis. Computational approaches are widely applied to drug development because of the increasing availability of biological molecular datasets. Popular generative approaches can create new drug molecules by learning the given molecule distributions. However, these approaches are mostly not for target-specific drug discovery. We developed an energy-based probabilistic model for computational target-specific drug discovery. Results show that our proposed TagMol can generate molecules with similar binding affinity scores as real molecules. GAT-based models showed faster and better learning relative to Graph Convolutional Network baseline models.