Considering x-axis as the internuclear axis, which out of the following will not form a sigma bond?

Will not form a $\mathrm{\sigma }$-bond. Because on taking x-axis as the internuclear axis, $2{\mathrm{p}}_{\mathrm{y}}\text{ and }2{\mathrm{p}}_{\mathrm{y}}$ orbitals overlap sideway (lateral overlapping) resulting in the formation of a $\mathrm{\pi }$-bond.