Lead-bismuth eutectic is used as a coolant for the fusion-fission hybrid system (FFS) based on a tokamak that enhances the transmutation of transuranic nuclides. However, this coolant does not produce enough tritium to supply the fusion reactions of the system. Therefore, the aim of this work is to evaluate the insertion of tritium breeder layers (TBLs) on the FFS to enhance tritium production. The analyzed materials for tritium production were beryllium, boron, and lithium alloys. The results indicate the most suitable material for tritium production depends on the TBL location. The results also indicate that there is a strong dependency on the position of the TBL affecting the neutronic parameters and nuclide transmutation such as criticality and fuel depletion. The reaction rates for tritium production and fuel composition after a fuel burnup were analyzed using the Monte Carlo N-Particle 5 (MCNP5) and MONTEBURNS codes.