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This paper is the second of a series that tackles the properties of moleculargas in galaxies residing in clusters and their related large-scale structures.Out of 21 targeted fields, 19 galaxies were detected in CO(3-2) with theAtacama Large Millimeter Array (ALMA), including two detections within a singlefield. These galaxies are either bona fide members of the CL1301.7$-$1139cluster ($z=0.4828$, $\sigma_{cl}=681$ km s$^{-1}$), or located within $\sim 7\times R_{200}$, its virial radius. They have been selected to sample the rangeof photometric local densities around CL1301.7$-$1139, with stellar massesabove log($M_{\rm star}$) = 10, and to be located in the blue clump ofstar-forming galaxies derived from the $u$, $g$, and $i$ photometric bands.Unlike previous works, our sample selection does not impose a minimum starformation rate or detection in the far-infrared. As such and as much aspossible, it delivers an unbiased view of the gas content of normalstar-forming galaxies at $z \sim 0.5$. Our study highlights the variety ofpaths to star formation quenching, and most likely the variety of physicalproperties (i.e. temperature, density) of the corresponding galaxy's coldmolecular gas. Just as in the case of CL1411.1$-$1148, although to a smallerextent, we identify a number of galaxies with lower gas fraction thanclassically found in other surveys. These galaxies can still be on thestar-forming main sequence. When these galaxies are not inside the clustervirialised region, we provide hints that they are linked to their infallregions within $\sim 4 \times R_{200}$.

SEEDisCS II. Molecular gas in galaxy clusters and their large scale structure: low gas fraction galaxies, the case of CL1301.7$-$1139