Arctic Sea ice variability arises from both anthropogenic forcing and natural climate modes such as the El Niño-Southern Oscillation (ENSO), North Atlantic Oscillation (NAO) and Arctic Oscillation (AO). While these modes are known to influence sea ice concentration (SIC) and thickness (SIT), their impacts on seasonal extremes remain less understood. In this study, the extreme SIC and SIT are investigated using ERA5 and CMEMS reanalysis products, applying a non-stationary generalised extreme value (GEV) framework with climate indices as covariates. Results indicate that winter and spring sea-ice variability is most pronounced in the Barents and Greenland Seas, where strong Atlantic inflows and dynamic atmospheric conditions make the marginal ice zone highly sensitive to even minor perturbations. Conversely, in the central and peripheral Arctic, variability maximises in summer and autumn, when melt processes, ice-albedo feedback and delayed freeze-up intensify interannual fluctuations. ENSO exerts notable seasonal effects: El Niño events enhance extreme SIC in the Laptev Sea but reduce it in the East Siberian Sea during summer, while SIT extremes increase in the Canadian Arctic Archipelago (CAA) and decline in the East Siberian Sea across all seasons. NAO-related anomalies include stronger SIC and SIT extremes in the Beaufort Sea and CAA and reductions in the Chukchi Sea during autumn. AO effects include increased SIC in the Chukchi Sea during summer and autumn, but decreases in the Beaufort and CAA in summer; SIT extremes rise in the CAA during spring but fall in the Beaufort Sea in summer. Composite analysis further reveals that out-of-phase NAO-AO states intensify autumn sea ice extremes, whereas in-phase conditions exert weaker influences. These results emphasise the distinct and seasonally varying roles of climate modes in shaping Arctic Sea ice extremes, offering insights into future Arctic climate variability.