The minimum error entropy (MEE) criterion is a powerful approach for non-Gaussian signal processing and robust machine learning. However, the instantiation of MEE on robust classification is a rather vacancy in the literature. The original MEE purely focuses on minimizing Renyi's quadratic entropy of the prediction errors, which could exhibit inferior capability in noisy classification tasks. To this end, we analyze the optimal error distribution with adverse outliers and introduce a specific codebook for restriction, which optimizes the error distribution toward the optimal case. Half-quadratic-based optimization and convergence analysis of the proposed learning criterion, called restricted MEE (RMEE), are provided. The experimental results considering logistic regression and extreme learning machine on synthetic data and UCI datasets, respectively, are presented to demonstrate the superior robustness of RMEE. Furthermore, we evaluate RMEE on a noisy electroencephalogram dataset, so as to strengthen its practical impact.