In today's machine learning (ML), the need for vast amounts of training data has become a significant challenge. Transfer learning (TL) offers a promising solution by leveraging knowledge across different domains/tasks, effectively addressing data scarcity. However, TL encounters computational and communication challenges in resource-constrained scenarios, and negative transfer (NT) can arise from specific data distributions. This article presents a novel focus on maximizing the accuracy of instance-based TL in multisource resource-constrained environments while mitigating NT, a key concern in TL. Previous studies have overlooked the impact of resource consumption in addressing the NT problem. To address these challenges, we introduce an optimization model named multisource resource-constrained optimized TL (MSOPTL), which employs a convex combination of empirical sources and target errors while considering feasibility and resource constraints. Moreover, we enhance one of the generalization error upper bounds in domain adaptation setting by demonstrating the potential to substitute the H ∆ H divergence with the Kullback-Leibler (KL) divergence. We utilize this enhanced error upper bound as one of the feasibility constraints of MSOPTL. Our suggested model can be applied as a versatile framework for various ML methods. Our approach is extensively validated in a neural network (NN)-based classification problem, demonstrating the efficiency of MSOPTL in achieving the desired trade-offs between TL's benefits and associated costs. This advancement holds tremendous potential for enhancing edge artificial intelligence (AI) applications in resource-constrained environments.