The focus of this paper is on multitask learning over adaptive networks where different clusters of nodes have different objectives. We propose an adaptive regularized diffusion strategy using Gaussian kernel regularization to enable the agents to learn about the objectives of their neighbors and to ignore misleading information. In this way, the nodes will be able to meet their objectives more accurately and improve the performance of the network. Simulation results are provided to illustrate the performance of the proposed adaptive regularization procedure in comparison with other implementations.