Some repeating fast radio burst (FRB) sources exhibit complex polarization behaviors, including frequency-dependent depolarization, variation of rotation measure (RM), and oscillating spectral structures of polarized components. Very recently, Feng et al. (2022) reported that active repeaters exhibit conspicuous frequency-dependent depolarization and a strong correlation between RM scatter (σ RM ) and the temporal scattering time (τ s ), σ RM ∝ τ 1.0±0.2 s , both of which can be well described by multipath propagation through a magnetized inhomogeneous plasma screen. This observation strongly suggests that the temporal scattering and RM scatter originate from the same region. Besides, a particular finding of note in Feng et al. ( 2022) is that the FRBs with compact persistent radio sources (PRS) tend to have extreme σ RM . In this work, we analyze the temporal scattering, RM scatter and the PRS emission contributed by the magnetized inhomogeneous plasma screen near an FRB source. The behaviors of the RM scatter imply that the magnetized plasma environment is consistent with a supernova remnant or a pulsar wind nebula, and the predicted σ RM -τ s relation is σ RM ∝ τ (0.54−0.83) s for different astrophysical scenarios. We also show that the specific luminosity of a PRS should have a positive correlation with the RM contributed by the plasma screen. This is consistent with the observations of FRB 121102 and FRB 190520B.