The dependence of the neutron yield of the FNS-ST (spherical tokamak) fusion neutron source on the fraction of tritium in the core D+T plasma is analyzed for the case of using tritium neutral beam injectors with 200-keV energy and 6-MW power. The FNS-ST operating regimes are explored using the SOLPS4.3 and ASTRA codes for different values of core plasma density ne, T fraction in the plasma, and particle diffusivity. The FC-FNS code is used to estimate the fluxes of the fuel components in the fuel cycle (FC), which are produced by different injection systems: gas puffing, pellet injection, and neutral beam (T) injection. It is shown that in the case of the Т beam injection, in the operating range of parameters, the neutron yield can reach 6.0 × 1017 s−1, which is the value comparable to that obtained for the scenario of D-beam injection into the balanced D+T plasma. In the case of the T-beam injection, in the range of parameters, for which the neutron yield is close to its maximum, the amount of tritium in the FC is lower than in the case of the D-beam injection. The neutron yield can be increased to 6.5 × 1017 n/s if full separation of the D and T is introduced for the gas pumped out from the divertor and puffed back into the torus. With this approach, in the case of the tritium beam, the amount of tritium in the FC is Tinv of ~170 g. If this approach is used in the case of the deuterium beam, the neutron yield can reach 7.0 × 1017 n/s. However, in this case, the amount of tritium contained in the FC increases to 215 g. The results of the analysis performed are used for optimizing the FC of the FNS-C (compact) fusion neutron source, which is planned for construction in the framework of the comprehensive program of the State Corporation Rosatom “Development of Engineering, Technology and Scientific Research in the Field of Using Atomic Energy in the Russian Federation for the Time Period up to 2030.”