In recent years, deep face recognition methods have demonstrated impressive results on in-the-wild datasets. However, these methods have shown a significant decline in performance when applied to real-world low-resolution benchmarks like TinyFace or SCFace. To address this challenge, we propose a novel classification consistency knowledge distillation approach that transfers the learned classifier from a high-resolution model to a low-resolution network. This approach helps in finding discriminative representations for low-resolution instances. To further improve the performance, we designed a knowledge distillation loss using the adaptive angular penalty inspired by the success of the popular angular margin loss function. The adaptive penalty reduces overfitting on low-resolution samples and alleviates the convergence issue of the model integrated with data augmentation. Additionally, we utilize an asymmetric cross-resolution learning approach based on the state-of-the-art semi-supervised representation learning paradigm to improve discriminability on low-resolution instances and prevent them from forming a cluster. Our proposed method outperforms state-of-the-art approaches on low-resolution benchmarks, with a three percent improvement on TinyFace while maintaining performance on high-resolution benchmarks.