  We study the quasinormal modes (QNMs) of charged scalar in the static
spherically symmetric black hole background near the event and cosmological
horizon. Starting with numerical analysis of the QNMs of black hole in the dRGT
massive gravity, the mathematical tool called the Asymptotic Iteration
Method~(AIM) is used to calculate the quasinormal frequencies. The parameters
such as the mass and charge of the black hole, the cosmological constant, the
coefficient of the linear term from massive gravity $\gamma$, and the mass of
the scalar are varied to study the behavior of the QNMs. We found the tower
pattern of the near-horizon quasinormal frequencies from the numerical results
by AIM where the real parts depend only on product of the charge of the black
hole and the scalar field and the imaginary parts depend only on the surface
gravity. To confirm the numerical finding, we analytically determine the exact
QNMs of the charged scalar near the horizons of any static spherically
symmetric black hole background in the simple universal forms; $\omega =
\displaystyle{\frac{qQ}{r_h}} + i \kappa_h n$ and $\omega =
\displaystyle{\frac{qQ}{r_c}} + i |\kappa_c| n$ where $n$ is a non-positive
integer and $\kappa_{h,c}$ is the surface gravity, for the event and
cosmological horizon respectively. Extending our analysis, we also compute the
four towers of the near-horizon QNMs that can reach the far region. The four
kinds of QNMs converge to certain asymptotic values with equally spacing
imaginary parts and the real parts proportional to $qQ/r_{h,c}$. These modes do
not match with the all-region~(WKB) modes of the real background since they are
originated from the linearly approximated metric.
