In‐depth understanding of human T‐cell‐mediated immunity in coronavirus disease 2019 (COVID‐19) is needed if we are to optimize vaccine strategies and immunotherapies. Identification of severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) T‐cell epitopes and generation of peptide–human leukocyte antigen (peptide–HLA) tetramers facilitate direct ex vivo analyses of SARS‐CoV‐2‐specific T cells and their T‐cell receptor (TCR) repertoires. We utilized a combination of peptide prediction and in vitro peptide stimulation to validate novel SARS‐CoV‐2 epitopes restricted by HLA‐A*24:02, one of the most prominent HLA class I alleles, especially in Indigenous and Asian populations. Of the peptides screened, three spike‐derived peptides generated CD8⁺IFNγ⁺ responses above background, S_1208–1216 (QYIKWPWYI), S_448–456 (NYNYLYRLF) and S_193–201 (VFKNIDGYF), with S₁₂₀₈ generating immunodominant CD8⁺IFNγ⁺ responses. Using peptide–HLA‐I tetramers, we performed direct ex vivo tetramer enrichment for HLA‐A*24:02‐restricted CD8⁺ T cells in COVID‐19 patients and prepandemic controls. The precursor frequencies for HLA‐A*24:02‐restricted epitopes were within the range previously observed for other SARS‐CoV‐2 epitopes for both COVID‐19 patients and prepandemic individuals. Naïve A24/SARS‐CoV‐2‐specific CD8⁺ T cells increased nearly 7.5‐fold above the average precursor frequency during COVID‐19, gaining effector and memory phenotypes. Ex vivo single‐cell analyses of TCRαβ repertoires found that the A24/S₄₄₈⁺CD8⁺ T‐cell TCRαβ repertoire was driven by a common TCRβ chain motif, whereas the A24/S₁₂₀₈⁺CD8⁺ TCRαβ repertoire was diverse across COVID‐19 patients. Our study provides an in depth characterization and important insights into SARS‐CoV‐2‐specific CD8⁺ T‐cell responses associated with a prominent HLA‐A*24:02 allomorph. This contributes to our knowledge on adaptive immune responses during primary COVID‐19 and could be exploited in vaccine or immunotherapeutic approaches.