  The scrutiny of black hole perturbations and its application to testing
gravity theories have been a very crucial frontier in modern physics. In this
paper we study the quasi-normal modes (QNM) of massless scalar perturbations
for various charged black holes in the Palatini-type theories of gravity.
Specifically, we consider the Palatini $f(R)$ theory coupled with Born-Infeld
nonlinear electrodynamics and the Eddington-inspired-Born-Infeld gravity (EiBI)
coupled with Maxwell electromagnetic fields. Special attention is paid to
Einstein-Born-Infeld black holes, EiBI charged black holes and Born-Infeld
charged black holes within $R\pm R^2$ gravity. These charged black holes are
shown to be stable and their quasi-normal frequencies, including the
frequencies in the eikonal limit, are calculated by using the WKB method up to
the 6th order. We compare the results with the Reissner-Nordstr\"om charged
black hole and prove that both the changes in the gravity sector and the matter
sector of the action alter the QNM spectra.
