Online vector quantization (VQ) method has been successfully applied to the kernel adaptive filters (KAFs) for curbing their linearly growing radial basis function (RBF) network, thereby generating a family of quantized KAFs (QKAFs). However, the most existing QKAFs are based on the mean square error (MSE) criterion, which is actually not a good choice for non-Gaussian signals. In this paper, a new quantized kernel adaptive filter called quantized kernel maximum correntropy (QKMC) is developed, which is robust to large outliers or impulsive noises. The mean square convergence analysis for QKMC is conducted, and a sufficient condition for guaranteeing convergence is therefore obtained. The filtering accuracy of QKMC is also proved to be higher than that of the representative quantized kernel least mean square (QKLMS). In addition, to make full use of the information hidden in the input and the output spaces, we further propose a modified QKMC based on bilateral gradient (QKMC-BG). To limit the final network size of QKMC-BG, the QXMC-BG with fixed budget (QKMC-BG-FB) is also developed. Simulation results under the cases of Gaussian and non-Gaussian noises are presented to validate the proposed QKMC, QKMC-BG and QKMC-BG-FB. (C) 2017 Elsevier Inc. All rights reserved.