Drug-target relationships may now be predicted computationally using bioinformatics data, which is a valuable tool for understanding pharmacological effects, enhancing drug development efficiency, and advancing related research. A number of structure-based, ligand-based and network-based approaches have now emerged. Furthermore, the integration of graph attention networks with intricate drug target studies is an application area of growing interest. In our work, we formulate a model called MKDTI by extracting kernel information from various layer embeddings of a graph attention network. This combination improves the prediction ability with respect to novel drug-target relationships. We first build a drug-target heterogeneous network using heterogeneous data of drugs and targets, and then use a self-enhanced multi-head graph attention network to extract potential features in each layer. Next, we utilize embeddings of each layer to computationally extract kernel matrices and fuse multiple kernel matrices. Finally, we use a Dual Laplacian Regularized Least Squares framework to forecast novel drug-target entity connections. This prediction can be facilitated by integrating the kernel matrix associated with the drug-target. We measured our model's efficacy using AUPR and AUC. Compared to the benchmark algorithms, our model outperforms them in the prediction outcomes. In addition, we conducted an experiment on kernel selection. The results show that the multi-kernel fusion approach combined with the kernel matrix generated by the graph attention network provides complementary insights into the model. The fusion of this information helps to enhance the accuracy of the predictions.