In this paper, we investigate the joint device activity and data detection in massive machine-type communications (mMTC) with a one-phase non-coherent scheme, where data bits are embedded in the pilot sequences and the base station simultaneously detects active devices and their embedded data bits without explicit channel estimation. Due to the correlated sparsity pattern introduced by the non-coherent transmission scheme, the traditional approximate message passing (AMP) algorithm cannot achieve satisfactory performance. Therefore, we propose a deep learning (DL) modified AMP network (DL-mAMPnet) that enhances the detection performance by effectively exploiting the pilot activity correlation. The DL-mAMPnet is constructed by unfolding the AMP algorithm into a feedforward neural network, which combines the principled mathematical model of the AMP algorithm with the powerful learning capability, thereby benefiting from the advantages of both techniques. Trainable parameters are introduced in the DL-mAMPnet to approximate the correlated sparsity pattern and the large-scale fading coefficient. Moreover, a refinement module is designed to further advance the performance by utilizing the spatial feature caused by the correlated sparsity pattern. Simulation results demonstrate that the proposed DL-mAMPnet can significantly outperform traditional algorithms in terms of the symbol error rate performance.