A three-dimensional dyadic Green's function is derived for electromagnetic scattering due to a point electric current source radiating in the vicinity of a wedge with anisotropic impedance and perfect electric conductor faces. The anisotropic impedance face is characterized by surface impedances along directions parallel and orthogonal to the edge axis (principal anisotropy axis). Arbitrary surface impedance is assumed in one direction only (either parallel or orthogonal to principal anisotropy axis), and vanishing impedance is assumed on the other. Assuming reactive surface impedance, the derived forms involve a summation over an angular wavenumber and a longitudinal spectral integral, which may be evaluated asymptotically to describe the fields in paraxial region, where the source and observation points are in close proximity to the apex but widely separated. The final asymptotic result reveals three different scattering mechanisms: edge-guided waves, surface waves, and guided waves in the classical sense. Numerical simulations are performed for capacitive and inductive surfaces using the asymptotic results. Simulation results are also compared to those of a commercially available electromagnetic field solver, which assumes uniform surface impedance.