Recently massless test scalar field perturbations of the holonomy corrected black holes [Z. Moreira et. al. Phys. Rev. D 107 (2023) 10, 104016] were studied in order to estimate quantum corrections to the quasinormal spectrum of a black hole. Here we study both the fundamental mode and overtones of scalar, electromagnetic and Dirac fields with the help of the Leaver method and higher order WKB formula with Pad\'e approximants. We observe that the overtones depend on the geometry near the event horizon, while the fundamental mode is localized near the peak of the potential barrier, what agrees with previous studies. We showed that unlike a massless field, the massive one possesses arbitrarily long lived modes. We also obtain the analytical eikonal formula for quasinormal modes and its extension beyond eikonal approximation as a series in powers of $1/\ell$, where $\ell$ is the multipole number.

The Bardeen black hole stands as the first model of a regular black hole. Driven by the interpretations of Bardeen spacetime as a quantum-corrected Schwarzschild-like solution, we study quasinormal modes of a massive scalar field within this context. We have found that the damping rate of the massive scalar field decreases as the mass grows, leading to appearance of the arbitrarily long lived modes. or quasiresonances. The massive term in the Bardeen case is distinctive also in two other respects. First, the overtones deviate from their massless limit at a much smaller rate than the fundamental mode, when the mass is turned on. This behavior overlaps with the outburst of overtones due to the quantum deformation near the event horizon. Finally, integration in the time-domain shows that the oscillatory tails decay as $\sim t^{-(\frac{8}{6}+\ell)}$ at intermediate times and as $\sim t^{-1}$ at asymptotically late times, which is different from the Reissner-Nordstr\"om and Schwarzschild limits.

We show that perturbations of a scalar field in the background of the black hole obtained with the Starobinsky-Bel-Robinson Gravity is unstable unless the dimensionless coupling $\beta$ describing the compactification of M-theory is small enough. In the sector of stability quasinormal spectrum show peculiar behavior both in the frequency and time domains: the ringing consists of two stages where two different modes dominate. The WKB method does not reproduce part of the spectrum including the fundamental mode, which is responsible for the first stage of the ringing. Consequently, the correspondence between the eikonal quasinormal modes and null geodesics allows to reproduce only part of the eikonal spectrum. The frequencies are obtained with the help of three methods (Frobenius, WKB and time-domain integration) with excellent agreement among them.