This study investigates the intrinsic spectra and energetics of twelve gamma-ray bursts (GRBs) with known redshifts detected by the BeppoSAX satellite. All GRBs were observed in a broad energy range (2–700 keV) and their spectra were well described by the Band model, with no significant soft X-ray excesses or spectral absorptions. The results show a positive correlation between the estimated total isotropic energy (E_rad) and redshift (z). More luminous GRBs also have higher peak energies (E_pS) in their EF(E) spectra. Additionally, more distant GRBs are systematically harder in the X-ray band compared to lower redshift GRBs. The study also finds a correlation between the low-energy photon index (α) and redshift, as well as between E_p and E_rad. The correlation between α and E_rad is weaker. The correlation coefficients between the logarithms of the quantities of interest are reported, showing strong correlations between log|α| and log(1+z), and between logE_p and logE_rad. These correlations remain significant even when excluding the most distant and energetic GRBs. The study discusses possible selection and data truncation effects that could bias the results. However, it concludes that the observed trends are likely not affected by these effects. The results suggest that the intrinsic properties of long GRBs are brighter and more energetic at larger distances. The study also finds that the peak energy (E_p) of GRBs is proportional to the total radiated energy (E_rad) with a power-law index of 0.52 ± 0.06. This relationship is consistent with the Optically Thin Synchrotron Shock Model (OTSSM) for certain electron distributions. The correlation between the low-energy photon index (α) and redshift is interpreted as a consequence of other correlations rather than a direct physical property of GRBs. The study concludes that the observed correlations are likely due to intrinsic properties of GRBs and not due to selection effects or data truncation.This study investigates the intrinsic spectra and energetics of twelve gamma-ray bursts (GRBs) with known redshifts detected by the BeppoSAX satellite. All GRBs were observed in a broad energy range (2–700 keV) and their spectra were well described by the Band model, with no significant soft X-ray excesses or spectral absorptions. The results show a positive correlation between the estimated total isotropic energy (E_rad) and redshift (z). More luminous GRBs also have higher peak energies (E_pS) in their EF(E) spectra. Additionally, more distant GRBs are systematically harder in the X-ray band compared to lower redshift GRBs. The study also finds a correlation between the low-energy photon index (α) and redshift, as well as between E_p and E_rad. The correlation between α and E_rad is weaker. The correlation coefficients between the logarithms of the quantities of interest are reported, showing strong correlations between log|α| and log(1+z), and between logE_p and logE_rad. These correlations remain significant even when excluding the most distant and energetic GRBs. The study discusses possible selection and data truncation effects that could bias the results. However, it concludes that the observed trends are likely not affected by these effects. The results suggest that the intrinsic properties of long GRBs are brighter and more energetic at larger distances. The study also finds that the peak energy (E_p) of GRBs is proportional to the total radiated energy (E_rad) with a power-law index of 0.52 ± 0.06. This relationship is consistent with the Optically Thin Synchrotron Shock Model (OTSSM) for certain electron distributions. The correlation between the low-energy photon index (α) and redshift is interpreted as a consequence of other correlations rather than a direct physical property of GRBs. The study concludes that the observed correlations are likely due to intrinsic properties of GRBs and not due to selection effects or data truncation.