The chemical composition of coal ash and the content of the critical elements Ga, Sc, and V in coal and ash are examined herein. In this study, lignite and bituminous coal from Polish deposits were used. The coals were subjected to ultimate and proximate analysis; the petrographic composition was determined based on maceral groups. The chemical composition of ash and the content of critical elements were determined using ICP-MS. The obtained results were correlated and Pearson’s linear correlation coefficient was determined. Based on the correlation analysis, the relationship between the chemical composition of ash and the proximate and ultimate analyses was demonstrated. The content of selected critical elements in the tested deposits was lower than the Clarke value in coal. However, in some deposits these contents are much higher in coal ashes. The higher levels of Ga, V, and Sc in the ash are associated with Al2O3. Therefore, it can be stated that ashes can be a potential source of some raw materials. The highest concentrations of critical elements in coal and ash were recorded in the Lublin Coal Basin. Supra-Clarke contents of Ga, V, and Sc were recorded in the Bogdanka coal mine.