To investigate the fatigue responses of key structural locations in a jacket-supported offshore wind turbine under combined wind and wave loading, a three-dimensional nonlinear finite element model of the NREL 5 MW turbine and its jacket foundation was developed in OpenSees. Time-domain analyses were conducted at six representative mean wind speeds ranging from 8.0 to 24.0 m/s while the baseline sea-state parameters were held constant. For each wind speed, 120 independent turbulent wind-field realizations were considered. The tower-base bending moment, axial force in the critical leg, and axial force in the critical brace were examined through peak and root-mean-square statistics, identification of statistically stable fatigue hotspots, damage-equivalent load calculations, rainflow counting, and power spectral density analysis. The effects of wave parameters and wind–wave angle were further investigated at the rated wind speed. The results show that mean wind speed is the dominant factor governing the fatigue responses. The three responses generally increase with wind speed but exhibit different degrees of local reduction near 16 m/s. For an S–N curve slope of m=3, and with the median DEL at 8 m/s used as the respective reference, the median normalized DELs of the tower-base bending moment, critical-leg axial force, and critical-brace axial force reach 4.726, 5.052, and 4.211 at 24 m/s, respectively. Brace hotspots remain concentrated in the upper jacket, whereas leg hotspots extend from the lower region toward the middle and upper regions as wind speed increases. The dominant frequencies of all three responses are approximately 0.244 Hz, closely matching the first structural natural frequency of 0.245 Hz. The tower-base bending-moment spectrum consists of numerous small-range cycles together with a limited number of larger-range cycles. The critical-leg axial force exhibits broad distributions of cycle mean and range, whereas the critical-brace axial force shows a pronounced mean-force bias. At the rated wind speed, the most energetic sea state considered, with Hs=6 m and Tp=11 s, increases the DELs of the tower-base bending moment and critical-leg axial force by 7.7% and 6.6% relative to the baseline sea state, respectively, while the change in the critical-brace axial-force DEL remains below 1%. The wind–wave angle has only a minor effect on the considered tower-base bending-moment component and critical-brace axial force. However, at a 90° wind–wave angle, the median paired normalized DEL of the critical-leg axial force reaches 1.600, corresponding to an increase of approximately 60.0% relative to the aligned 0° condition, and its 90th percentile is approximately 2.05. These findings provide a basis for identifying fatigue-sensitive components, improving component-level design, and selecting monitoring locations for jacket-supported offshore wind turbines.