The quantum-mechanical phase difference across the barrier of an annular, i.e. ring shaped Josephson tunnel junctions obeys to periodic boundary conditions which fix the algebraic sum of fluxons and antifluxons trapped in the barrier so that only fluxon-antifluxon pairs can be nucleated or annihilated. In gapped annular Josephson tunnel junctions this constrain is removed and single fluxons or antifluxon can be nucleated or annihilated resulting in altered static and dynamic phase properties. We present a detailed theoretical and experimental study of the magnetic patterns and of the Fiske resonances in gapped annular Josephson tunnel of different length and geometrical configurations.