The Normalized Difference Snow Index (NDSI) is essential for accurate snow monitoring, but the widely used MODIS NDSI products generally have significant data gaps mainly due to cloud cover. Existing gap-filling methods often introduce artifact issue in regions with extensive and persistent cloud cover, where gap areas produce inaccurate results influenced by cloud shapes. To address NDSI gap-filling issue, we developed a mask-aware Transformer integrating multi-source data (MAT-MS) to effectively fill these gaps in MODIS NDSI data. The MAT-MS model leverages spatiotemporal information related to meteorology, topography, and geographic location. By incorporating a mask-aware technique, the MAT-MS can learn cloud shapes and patterns, helping to mitigate the common artifact issue. Validation using data from the Tibetan Plateau demonstrated the superior performance of the MAT-MS model, with averaged MAE, RMSE, and R² of 1.585, 5.531, and 0.868, respectively. The model reduced RMSE by over 30 % compared to traditional spatiotemporal interpolation methods, and by 9 % compared to mainstream deep learning models. Using MAT-MS, we generated a daily gap-free NDSI dataset for the Tibetan Plateau spanning from 2003 to 2020. This spatiotemporally continuous dataset is critical for detailed snow identification, enabling enhanced estimates of snow cover area, fractional snow cover, and snow depth. The flexibility of the MAT-MS model also makes it applicable to a wide range of continuous remote sensing datasets affected by data gaps.