In recent years,community search on heterogeneous information networks has attracted more and more attention and has been widely used in graph data analysis.However,the existing community search problems on heterogeneous information networks do not consider the fairness of attributes on subgraphs.In this work,we combine attribute fairness with kPcore mining on heterogeneous information networks and propose a maximum core mining problem on heterogeneous information networks based on attribute fairness for the first time.To solve this problem,we propose a new subgraph model called FkPcore.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,we propose the Adv-FkPcore algorithm to avoid judging all kPcores and their subgraphs when enumerating FkPcores.In addition,in order to improve the acquisition efficiency of P_neighbor,we propose a traversal method with vertex sign (TMS) and propose a new FkPcore enumeration algorithm called Opt-FkPcore based on the TMS algorithm.A large number of experiments on heterogeneous information networks demonstrate the effectiveness and efficiency of our proposed method.