The collective magnetoplasmon polariton excitations in a semiconductor superlattice with the thicknesses arranged in Thue-Morse sequence are studied. We take the effect of retardation into account and assume the system is subjected to an external static magnetic field applied parallel to the interfaces. It is found that the spectrum of the polariton has the Canter-like structure, and the total widths of the bands show scaling properties with increasing the generation. The external magnetic field makes the bands become mole narrow and shift to higher frequencies for the optical modes and to lower frequencies for the acoustic modes. For a given excitation frequency, the localization properties of the modes will be changed if we vary the external field.
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