Based on the generalized reduced R-matrix theory, this work performs a comprehensive analysis of all available experimental data for the ⁶He system by using the R-matrix analysis code (RAC). A complete set of evaluated nuclear data is obtained for major reaction channels induced by triton beams in an energy range of 10^–2—20 MeV. The evaluated integral cross sections include T(t, 2n)⁴He, T(t, n)⁵He, and T(t, d)⁴H reactions, and the differential cross sections include T(t, 2n)⁴He, T(t, n)⁵He, T(t, d)⁴H, and T(t, t)T. The evaluation results show that they are in good agreement with experimental data and the evaluated data of ENDF/B-VIII.1. In particular, for the T(t, 2n)⁴He reaction, the evaluated cross sections are consistent with the existing experimental results over the full energy range, and a resonance dominated by the 2⁺ level is observed near 2.9 MeV. At 1.9 MeV, where experimental measurements of both integral cross sections and angular distributions are available, the evaluation accurately reproduces both observables. The combined constraint of integral and differential data significantly improves the stability of R-matrix parameters and the reliability of the evaluation. Based on the global analysis of the ⁶He system, this work also provides supplementary cross section data for the T(t, n)⁵He and T(t, d)⁴H reactions. The results contribute to the nuclear data foundation for fusion-related reactions and lay the groundwork for future joint evaluation with the mirror ⁶Be system.The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00202.