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Six-dimensional chiral gauged Einstein-Maxwell supergravity admits a two-parameter rotating dyonic string solution whose near horizon limit is the direct product of three-dimensional Anti-De Sitter space and a squashed three-sphere $S^3$. For a particular relation between the two parameters, the solution preserves $1/2$supersymmetry. We determine the complete Kaluza-Klein spectrum of the theory around these ${\mathrm{AdS}}_3$backgrounds. For the supersymmetric backgrounds, the states organize into infinite towers of long and short multiplets of $\mathrm{OSp}\left(2\right|2)$. In a certain limit of parameters, both the supersymmetric and the nonsupersymmetric spectra exhibit scale separation. In the latter case there are five topologically massive vectors and five scalars retaining finite masses with integer conformal dimensions, and in the supersymmetric case there are supersymmetric partners with half integer conformal dimensions, while all other masses diverge. Published by the American Physical Society2025