New Unfolded Higher Spin Systems in $AdS_3$

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.