•We develop harmonic background field extension based on physics-informed GAN.•Our method mitigates propagated error from background field removal in limited FOV.•Physics-informed loss shows improved results of extended harmonic field.•Outperforms conventional background field removal algorithms alone in limited FOV.•Overcomes susceptibility underestimation of QSM in limited FOV. Quantitative susceptibility mapping (QSM) is frequently employed in investigating brain iron related to brain development and diseases within deep gray matter (DGM). Nonetheless, the acquisition of whole-brain QSM data is time-intensive. An alternative approach, focusing the QSM specifically on areas of interest such as the DGM by reducing the field-of-view (FOV), can significantly decrease scan times. However, severe susceptibility value underestimations have been reported during QSM reconstruction with a limited FOV, largely attributable to artifacts from incorrect background field removal in the boundary region. This presents a considerable barrier to the clinical use of QSM with small spatial coverages using conventional methods alone. To mitigate the propagation of these errors, we proposed a harmonic field extension method based on a physics-informed generative adversarial network. Both quantitative and qualitative results demonstrate that our method outperforms conventional methods and delivers results comparable to those obtained with full FOV. Furthermore, we demonstrate the versatility of our method by applying it to data acquired prospectively with limited FOV and to data from patients with Parkinson's disease. The method has shown significant improvements in local field results, with QSM outcomes. In a clear illustration of its feasibility and effectiveness in real clinical environments, our proposed method addresses the prevalent issue of susceptibility underestimation in QSM with small spatial coverage.