  We report the neutron scattering results on magnetic orderings and
excitations in $\mathrm{Ba}_2\mathrm{CoTeO}_6$ composed of two almost isolated
subsystems A and B, which are described as an $S\,{=}\,1/2$ triangular
Heisenberg-like antiferromagnet and a frustrated honeycomb Ising-like
antiferromagnet, respectively. Stripy ordering of subsystem B was confirmed
below $T_{\rm N1}\,{=}\,12.0$ K, whereas sharp streaks were observed along
$(1/3, 1/3, L)$ and $(2/3, 2/3, L)$ at 0.3 K (${\ll}\,T_{\rm N2}\,{=}\,3.0$ K).
This indicates the two-dimensional nature of ordering in subsystem A. It was
found that the excitation spectra of both subsystems are well separated and
independent of each other. The excitation spectrum of subsystem A is composed
of two single-magnon branches with roton-like minima at the M point and a
clearly structured intense continuum, as similarly observed in
$\mathrm{Ba}_3\mathrm{CoSb}_2\mathrm{O}_9$, which is strongly indicative of
spinon excitations. Dispersion curves for subsystem B can be described by
linear spin wave theory within the third-neighbor exchange interaction.
