  Motivated by recent reports of a field-induced intermediate phase (IP) in the
antiferromagnetic honeycomb Kitaev model that may be a spin liquid whose nature
is distinct from the Kitaev Z2 phase, we present a detailed numerical study on
the nature and dynamical response (such as dynamical spin-structure factors and
resonant inelastic x-ray scattering intensities) of this field-induced IP and
neighboring phases in a family of Kitaev-based models related by hidden
symmetries and duality transformations. We further show that the same
field-induced IP can appear in models relevant for $\alpha$-RuCl${_3}$, which
exhibit a ferromagnetic Kitaev coupling and additional interactions. In
$\alpha$-RuCl${_3}$, the IP represents a new phase, that is likely independent
from the putative field-induced (spin-liquid) phase recently reported from
thermal Hall conductivity measurements.
