The turbulent transport properties and dynamics of zonal flows (ZFs) in the presence of fast ions (FIs) are investigated for a typical internal transport barrier (ITB) plasma based on the gyrokinetic approach, focusing on the role of FI temperature and the effects of the toroidal rotation, including the E× B rotational shear, parallel velocity gradient (PVG) as well as the rotation velocity itself. Linear GENE simulations have shown that the core ITB plasma on HL-2A is dominated by ion temperature gradient (ITG) modes and trapped electron modes (TEMs), where the former is stabilized by FIs whereas destabilized by the PVG. Neither of the FIs or the PVG has observable effect on TEMs. The ion heat transport generally decreases at large FI temperature due to the nonlinear electromagnetic stabilization of turbulence with increased total plasma β until electromagnetic modes are excited. The transport fluxes peak around a certain FI temperature and the ZF shearing rate is significantly higher at such value compared with that in the absence of FIs, and the heat flux reduction is a result of the synergistic interaction between turbulence, ZFs and the external rotational shear. The E× B shear stabilizing and PVG destabilizing is not obvious at low normalized ITG R/LTi, indicating they are less important in determining the stiffness level in the relatively low density and rotation scenarios regarding the HL-2A ITB discharges. The turbulence suppression is predominated by the nonlinear stabilization of ITG turbulence as well as enhanced ZFs simultaneously in the presence of FIs. These results have also provided the possible way to reduce the turbulence transport through increasing the FI temperature in the off-axis neutral beam heated plasmas such as in HL-2A.