T cells recognize several types of antigens in tumors, including aberrantly expressed, nonmutated proteins, which are therefore shared with normal tissue and referred to as self/shared-antigens (SSA), and mutated proteins or oncogenic viral proteins, which are referred to as tumor-specific antigens (TSA). Immunotherapies such as immune checkpoint blockade (ICB) can activate T-cell responses against TSA, leading to tumor control, and also against SSA, causing immune-related adverse events (irAE). To improve anti-TSA immunity while limiting anti-SSA autoreactivity, we need to understand how tumor-specific CD8+ T cells (TST) and SSA-specific CD8+ T (SST) cells differentiate in response to cognate antigens during tumorigenesis. Therefore, we developed a genetic cancer mouse model in which we can track TST and SST differentiation longitudinally as liver cancers develop. We found that both TST and SST lost effector function over time, but while TST persisted long term and had a dysfunctional/exhausted phenotype (including expression of PD1, CD39, and TOX), SST exited cell cycle prematurely and disappeared from liver lesions. However, SST persisted in spleens in a dysfunctional TCF1+PD-1- state: unable to produce effector cytokines or proliferate in response to ICB targeting PD-1 or PD-L1. Thus, our studies identify a dysfunctional T-cell state occupied by T cells reactive to SSA: a TCF1+PD-1- state lacking in effector function, demonstrating that the type/specificity of tumor antigen may determine tumor-reactive T-cell differentiation.