Chronic antigen exposure during viral infection or cancer promotes an exhausted T cell (Tex) state with reduced effector function. However, whether all antigen-specific T cell clones follow the same Tex differentiation trajectory remains unclear. Here, we generate a single-cell multiomic atlas of T cell exhaustion in murine chronic viral infection that redefines Tex phenotypic diversity, including two late-stage Tex subsets with either a terminal exhaustion (Tex^term) or a killer cell lectin-like receptor-expressing cytotoxic (Tex^KLR) phenotype. We use paired single-cell RNA and T cell receptor sequencing to uncover clonal differentiation trajectories of Tex^term-biased, Tex^KLR-biased or divergent clones that acquire both phenotypes. We show that high T cell receptor signaling avidity correlates with Tex^term, whereas low avidity correlates with effector-like Tex^KLR fate. Finally, we identify similar clonal differentiation trajectories in human tumor-infiltrating lymphocytes. These findings reveal clonal heterogeneity in the T cell response to chronic antigen that influences Tex fates and persistence.