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Quasinormal modes of scalar, electromagnetic, and gravitational fields in theextreme Schwarzschild-de Sitter background are known to be expressed inanalytic form as eigenvalues of the P\"oschl-Teller wavelike equation. We showthat perturbations of fermionic fields (given by Dirac and Rarita-Schwingerequations) do not lead to the P\"oschl-Teller effective potential.Nevertheless, using the Frobenius method we find quasinormal modes analyticallyin this case as well. We write down the analytical formula for quasinormalfrequencies of the near-extreme Schwarzschild-de Sitter black holes, which isvalid for both bosonic and fermionic fields. We further extend the analysis tothe case of charged rotating black holes and find a general analytical formulafor quasinormal modes of the fields of various spin for the near extremeKerr-Newman-de Sitter spacetime.

Analytic formula for quasinormal modes in the near-extreme Kerr-Newman-de Sitter spacetime governed by a non-P\"oschl-Teller potential