Perturbations in the parametrized wormhole spacetime and their related quasinormal modes

We study electromagnetic perturbations and the associated quasinormal modes (QNMs) of parametrized static, spherically symmetric wormhole spacetimes, focusing on Damour-Solodukhin and braneworld geometries as well as their galactic extensions. Using the Bronnikov-Konoplya-Pappas parametrization, we express the metric functions in terms of a compactified radial coordinate and characterize the spacetime through far-field and near-throat parameters. The far-field coefficients govern the asymptotic structure and post-Newtonian behaviour, while the near-throat continued-fraction expansion captures the strong-field geometry near the throat. We first apply the parametrization to isolated wormholes and identify its range of validity, showing that non-polynomial metric functions can limit the convergence of the near-throat expansion and hence the accuracy of a truncated representation. We then extend the framework to a galactic Damour-Solodukhin wormhole embedded in a Hernquist dark matter halo. Imposing observational bounds from the shadow of Sgr A*, we constrain the galactic compactness and deformation parameters and obtain an observationally viable parametrized metric. Within the allowed parameter space, we compute the fundamental QNM frequencies using the transfer matrix method and analyze the corresponding time-domain ringdown signals. We find that the damping rate is more sensitive to galactic compactness, whereas the oscillation frequency remains comparatively stable. Although the spectral shifts are small within the shadow-allowed region, the framework provides a systematic link between geometric parametrization, shadow constraints, and dynamical response. Our results establish an observationally consistent parametrized description of wormhole perturbations for strong-field tests of horizonless compact objects.