In recent years, community search on heterogeneous information networks has attracted more and more attention and has been widely used in graph data analysis. Nevertheless, the existing community search problems on heterogeneous information networks do not consider the fairness of attributes on subgraphs. This work combines attribute fairness with kPcore mining on heterogeneous information networks and proposes a maximum core mining problem on heterogeneous information networks based on attribute fairness. To solve this problem, a subgraph model called FkPcore is proposed. When enumerating FkPcore, the basic algorithm called Basic-FkPcore traverses all path instances and enumerates a large number of kPcores and their subgraphs. In order to improve the efficiency of the algorithm, an Adv-FkPcore algorithm is proposed to avoid judging all kPcores and their subgraphs when enumerating FkPcores. In addition, in order to improve the acquisition efficiency of P_neighbor, a traversal method with vertex sign (TMS) and a FkPcore enumeration algorithm called Opt-FkPcore based on the TMS algorithm are proposed. A large number of experiments on heterogeneous information networks demonstrate the effectiveness and efficiency of the proposed method.