Suppression of the antiferromagnetic order by Zn doping in a possible Kitaev material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>Na</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi>Co</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi>TeO</mml:mi></mml:mrow><mml:mn>6</mml:mn></mml:msub></mml:math>

Very recently, a $3d$ based honeycomb cobaltate ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ has garnered tremendous attention due to the proposed proximity Kitaev spin-liquid state as its $4d/5d$ counterparts. Here, we use Zn substitute Co in broad range and perform systematic studies on ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{TeO}}_{6}$ by structural, magnetic, thermodynamic measurements, track doping evolution of magnetic ground states. Due extremely close radii ${\mathrm{Zn}}^{2+}$ high-spin ${\mathrm{Co}}^{2+}$ ions, substitution can be easily achieved. X-ray diffractions reveal no structural transition but only minor changes lattice parameter $c$ over wide $0\ensuremath{\le}x\ensuremath{\le}1.5$. Magnetic susceptibility specific heat measurements both suggest an antiferromagnetic which is gradually suppressed with doping. It survive $x$ up $\ensuremath{\sim}1.0$. Then it evolves into spin-glass phase short-range order that rapidly supplanted magnetically disordered when $x\ensuremath{\ge}1.3$. By summarizing all these data, construct diagram ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{TeO}}_{6}$. Our results demonstrate effectively suppress induce possible quantum paramagnetic state. These may serve platform investigate physics this system.