In modern power distribution systems, the need for information and communication technology (ICT)-integrated control strategies has grown because of the growing use of inverter-based resources (IBRs), especially grid-forming converters (GFMCs). While these technologies enhance grid flexibility and efficiency, they also expand the grid’s vulnerability to cyberattacks, introducing new challenges to the reliability and security of power systems. This article introduces a robust distributed learning framework for stabilizing voltage and frequency and supporting effective power sharing in GFMCs under false data injection attacks (FDIAs). To mitigate the harmful impacts of disturbances and attacks, a distributed $\mathcal{H}_{\infty}$ control is implemented. By incorporating a learning-based neural network (NN) approximator with distributed robust $\mathcal{H}_{\infty}$ control, resilience and stability against cyberattacks in the secondary control layer of the GFMC are enhanced. The proposed method employs a learning-based approximator to estimate attack signals, while a distributed robust $\mathcal{H}_{\infty}$ control attenuates the effects of disturbances to guarantee robust stability. This approach also enables an accurate estimation of the attack signals despite external disturbances, satisfying the $\mathcal{L}_{2}$-gain condition for the tracking error. The method’s effectiveness is validated through simulation and hardware-in-the-loop (HIL) testing.<p></p>