  Identifying the exotic quantum spin liquid phase in Kitaev magnets has
garnered great research interests and remains a significant challenge. In
experiments, most of the proposed candidate materials exhibit an
antiferromagnetic (AFM) order at low temperatures, thus the challenge
transforms into the searching for a field-driven disordered phase that is
distinct from the partially polarized paramagnetic phase after suppressing the
AFM order. Recently, Na$_2$Co$_2$TeO$_6$ has been proposed as one of the prime
candidates, where the Kitaev interaction is realized by the high-spin
$t^{5}_{2g}e^2_g$ configuration, and spin-orbit entangled $J_{\rm eff} = 1/2$
state in a bond-edge shared honeycomb lattice. In this study, we identify an
emergent intermediate disordered phase induced by an external field along the
$c$-axis of the honeycomb plane. This phase is characterized through
magnetization and magnetocaloric effect experiments in high magnetic fields. To
explain the experimental results, we propose an effective spin model with large
AFM Kitaev interaction, which yields results in good agreement with both our
findings and previously reported data. We determine that the effective
$K$-$J$-$\Gamma$-$\Gamma'$ model for Na$_2$Co$_2$TeO$_6$ is nearly dual to that
of $\alpha$-RuCl$_3$ under an unitary transformation. Given the insignificant
fragility of Na$_2$Co$_2$TeO$_6$ sample, further high-field experiments can be
conducted to explore this intermediate-field quantum spin disordered phase.
