In bottom-up proteomics, peptide-spectrum matching is critical for peptide and protein identification. Recently, deep learning models have been used to predict tandem mass spectra of peptides, with the similarity scores of predicted and experimental spectra being integrated into peptide-spectrum matching. These models follow the supervised learning paradigm, which trains a general model using paired peptides and spectra from standard datasets and uses the model for prediction on experimental data. However, this approach can lead to inaccurate predictions due to differences between the training data and the experimental data, such as sample types, enzyme specificity, and instrument calibration. To address this issue, we proposed a Test-Time Training paradigm that adapts the pre-trained model to experimental data-specific models, namely PepT3. PepT3 results in a 10-40\% increase in peptide identification, depending on the distinctness of training and experimental data. Intriguingly, PepT3 improves the identification of tumor-specific neo-epitopes when applied to a complex patient-derived immunopeptidomic sample, with two-thirds of these neo-epitopes predicted to bind to the patient's human leukocyte antigen isoforms