Rotational symmetry breaking at the incommensurate charge-density-wave transition in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Ba</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>Ni</mml:mi><mml:mo>,</mml:mo><mml:mi>Co</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>As</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msub></…

Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,\@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,\@ non-magnetic analog BaFe$_2$As$_2$ structural same temperature range,\@ share common tetragonal aristotype crystal structure space-group type $I4/mmm$.\@ In contrast to where collinear stripe order is found for orthorhombic low-$T$ phase, unidirectional charge density wave together (distorted) zig-zag chains are observed triclinic BaNi$_2$As$_2$.\@ Here we show that between high- phases Ba(Ni,Co)$_2$(As,P)$_2$ additional broken fourfold symmetry $d_{xz}$ orbital exists which promising candidate charge/orbital-fluctuation-induced nematicity. Moreover, our data suggest enhanced $T_{\rm c}$ higher Co or P substitution levels might result from suppression reducing contribution $d_{xy}$ orbitals.