We screened six cobalt-based 18-VEC systems CoVSi, CoNbSi, CoTaSi (Si-group) and CoVGe, CoNbGe, CoTaGe (Ge-group) by the first-principles approach, with the motivation of stabilizing these orthorhombic phases into the cubic symmetry -favorable for thermoelectrics. Remarkably, it was found that the Ge-group is energetically more favorable in the cubic symmetry than the hitherto orthorhombic phase. We account the cubic ground state of the Si-group to the interplay of internal pressure and covalent interactions. The principle of covalent interactions will provide an insight and could be vital in speeding the search of missing cubic half-Heusler alloys. Meanwhile, the calculated transport properties of all the systems on p-type doping, except CoVSi, are more promising than the well-known CoTiSb. We also provide conservative estimates of the figure of merit, exceeding the CoTiSb. Based on our findings, we suggest possible new phases of ternary compounds for thermoelectric applications.Usage: Secondary publications and information retrieval purposes.PACS numbers: May be entered using the \pacs{#1} command.Structure: You may use the description environment to structure your abstract; use the optional argument of the \item command to give the category of each item. * S.S. and M.Z. contributed equally to this work. † Corresponding author: hem12fcy[at]iitr.ac.in