We consider the effects of an external magnetic field on the plasmon polaritons in finite quasiperiodic superlattices consisting of alternate degenerate semiconductor or metallic layers. The magnetic field is applied parallel to the interfaces. A type of magnetoplasmon polariton that is not present in the conductor-insulator-conductor configuration is discussed. The spectrum is composed of three main bands in which the modes exhibit different localization properties. The modes at higher frequency are extended, but those at lower frequency are critical or localized. Some surface modes have been found in the finite system.