  We investigate the unfolded formulation of bosonic Lorentz tensor fields of
arbitrary spin in $AdS_3$ containing a parity breaking mass parameter. They
include deformations of the linearisations of the Prokushkin--Vasiliev higher
spin theory around its critical points. They also provide unfolded formulations
of linearized topologically massive higher spin fields including their critical
versions. The gauge invariant degrees of freedom are captured by infinite
towers of zero forms. We also introduce two inequivalent sets of gauge
potentials given by trace constrained Fronsdal fields and trace unconstrained
metric-like fields.
