The distribution of baryons provides a significant way to understand the formation of galaxy clusters by revealing the details of its internal structure and changes over time. In this paper, we present theoretical studies on the scaled profiles of physical properties associated with the baryonic components, including gas density, temperature, metallicity, pressure and entropy as well as stellar mass, metallicity and satellite galaxy number density in galaxy clusters from z = 4 to z = 0 by tracking their progenitors. These mass-complete simulated galaxy clusters are coming from THE THREE HUNDRED with two runs: GIZMO-SIMBA and GADGET-X. Through comparisons between the two simulations, and with observed profiles that are generally available at low redshift, we find that (1) the agreements between the two runs and observations are mostly at outer radii r ≿ 0.3r500, in line with the self-similarity assumption. While GADGET-X shows better agreements with the observed gas profiles in the central regions compared to GIZMO-SIMBA; (2) the evolution trends are generally consistent between the two simulations with slightly better consistency at outer radii. In detail, the gas density profile shows less discrepancy than the temperature and entropy profiles at high redshift. The differences in the cluster centre and gas properties imply different behaviours of the AGN models between GADGET-X and GIZMO-SIMBA, with the latter, maybe too strong for this cluster simulation. The high-redshift difference may be caused by the star formation and feedback models or hydrodynamics treatment, which requires observation constraints and understanding.
