Observing the interstellar medium (ISM) in $z gtrsim 6$ quasars host galaxies is essential for understanding the co-evolution between the supermassive black holes and their hosts. To probe the gas physical conditions and search for imprints of Active Galactic Nuclei (AGN) on the ISM, we report ALMA observations of the $rm [N II]_{122 mu m}$ and $rm [O I]_{146 mu m}$ lines and the underlying continuum from the $z=6.003$ quasar SDSS J231038.88+185519.7. Together with previous $rm [C II]_{158 mu m}$ and $rm [O III]_{88 mu m}$ observations, we use the ratios of these fine-structure lines to probe the ISM properties. Similar to other high-$z$ systems, this object exhibits a $rm [C II]_{158 mu m}$/$rm [O I]_{146 mu m}$ ratio comparable to the lowest values found in local (Ultra) luminous infrared galaxies, suggesting a warmer and denser gas component compared to typical local systems. The $rm [O III]_{88 mu m}$/$rm [O I]_{146 mu m}$ ratio is lower than that of other local and high-$z$ systems, indicating a smaller ionized gas fraction in this quasar. The $rm [O III]_{88 mu m}$/$rm [N II]_{122 mu m}$ ratio is comparable to that of local systems, and suggests a metallicity of $Z/Z_{odot}$=1.5$-$2.1. Based on the $rm [N II]_{122 mu m}$ detection, we estimate that $17%$ of the $rm [C II]_{158 mu m}$ emission is associated with ionized gas. The $rm [N II]_{122 mu m}$ line shows a flux deficit comparable to local systems. The $rm [O I]_{146 mu m}$ line, with a $rm [O I]_{146 mu m}$/FIR ratio $ge 2times$ than expected from the local relation, indicates no $rm [O I]_{rm 146 mu m}$ deficit. The low $rm [C II]_{158 mu m}$/$rm [O I]_{146 mu m}$ ratio, together with the high $rm [O I]_{146 mu m}$/FIR ratio in J2310+1855, reveals that the warm and dense gas is likely a result of AGN heating to the ISM.
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