Quasinormal modes of magnetized black hole

We investigate charged, massive scalar field around static, spherically symmetric black hole immersed into an external asymptotically uniform magnetic field $B$. It is shown that for given multipole number $\mathrm{\ell }$ there are $2\mathrm{\ell }+1$ numbers of modes due to the Zeeman effect appearing by an interaction of the external magnetic and charged scalar fields introducing an effective mass of the scalar field ${\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}=\sqrt{{\mu }^2-mqB}$ where $m$ is the azimuthal number and $q$ is the charge coupling constant. We calculate threshold value of effective mass in which quasinormal modes are arbitrarily long lived and beyond that value quasinormal modes vanish. In the case of $m qB<0$ quasinormal modes are longer lived with larger oscillation frequencies. Whenever, magnetic and massive scalar fields satisfies condition $\mu_{\rm eff}^2<0$,aninstabilityappears,i\mathrm{.}e\mathrm{.},if$qB>0$or$qB<0$ there is an instability for the values of azimuthal number $m>{\mu }^2\mathrm{/}qB$ or $m<{\mu }^2\mathrm{/}qB$, respectively.