Aims. We aim to study the interstellar medium (ISM) and cosmic-rays (CRs) in a mid-latitude region in the third Galactic quadrant (Galactic longitude $l$ from $200{\mbox{$^\circ$}}$ to $260{\mbox{$^\circ$}}$ and latitude $|b|$ from $22{\mbox{$^\circ$}}$ to $60{\mbox{$^\circ$}}$ ). The region is expected to be dominated by local HI clouds since it is located at high latitude and free of know large molecular clouds.\\ Methods. We evaluated the total gas column density $N({\rm H_{tot}})$ by investigating the correlations among 21~cm survey data (HI4PI), Planck dust thermal emission models (optical depth at 353~GHz $\tau_{353}$ and radiance $R$), and Fermi-LAT $\gamma$-ray data in the region studied.
In the South region, we first masked areas containing an intermediate velocity cloud or the Orion-Eridanus superbubble, and that with a ratio of the integrated HI 21-cm line intensity to dust emission significantly different from that seen in the rest of the region.
We then fit the $\gamma$-ray data with a linear combination of gas template maps based on Planck dust models and other components to obtain the total gas column density $N({\rm H}_{{\rm tot},\gamma})$.\\ Results & Prospects. We found that
$N({\rm H}_{{\rm tot},\gamma})$/$\tau_{353}$ and $N({\rm H}_{{\rm tot},\gamma})$/$R$ depend on dust temperature $T_{\rm d}$ in the North region, indicating that that neither $\tau_{353}$ nor $R$ were proportional to $N({\rm H_{tot}})$.
We also found that $N({\rm H}_{{\rm tot},\gamma})$ is not proportional to $\tau_{353}$ but shows non-linear relation in the South region.
We will examine the systematic uncertainties and discuss ISM and CR properties inferred from $\gamma$-ray data.\\