take into account the Abrikosov vortices trapping during the thermal quench as a compet- itive effect [25]. In addition, a new detection principle based on the interaction of a single gamma-photon with trapped Abrikosov vortex is proposed for the development of a gamma -ray solid state detector with high intrinsic detection efficiency in the energy range up to 100 keV [26]. In this paper we present a theoretical study of the Fiske steps for a ”small” Josephson junctions in the presence of randomly distributed Abrikosov vortices. Our approach is based on the extension of a well known Kulik analysis for low-dissipative uniform Josephson junctions [27] to the Josephson junctions with inhomogeneities. We obtain a peculiar regime where the Fiske steps amplitude shows a weak non-monotonic decrease with the vortex density n$_{A}$ . We experimentally trapped different number of Abrikosov vortices and for each vortex density n$_{A}$ we measured the dependencies of the critical current I$_{c}$ and the Fiske steps amplitude I$_{F}$ on n$_{A}$ and on externally applied parallel to the junction plane magnetic field B$_{‖}$ . A good agreement between our theory and experimental results was found. The paper is organized as follows. In section II the theoretical model of a Josephson junction with randomly distributed misaligned Abrikosov vortices is presented. In section III by making use of a generic approach elaborated in the Ref. [27], we calculate the Fiske resonances in inhomogeneous Josephson junctions, and in the section IV the dependence of the Fiske steps amplitude I$_{F}$ on the density of Abrikosov vortices n$_{A}$ is analyzed. Section V is dedicated to the experimental details, namely, the experimental setup, the sample description and the procedure to measure the Josephson critical current I$_{c}$ and the amplitude of first Fiske step I$_{F}$ . In section VI we present the experimental results and the comparison with the theory. Section VII provides conclusions. We consider a small, i.e. W < λ$_{J}$ , Josephson junction in the presence of randomly distributed pinned misaligned Abrikosov vortices (here, W is the size of a Josephson junction, and λ$_{J}$ is the Josephson penetration depth). A magnetic field of a misaligned Abrikosov vortex enters and leaves the superconducting electrodes of a junction in different points. The distance between these points determines the misalignment length δ (see Fig. 1). 4 II. MODEL OF A JOSEPHSON JUNCTION WITH RANDOMLY DIS- TRIBUTED MISALIGNED ABRIKOSOV VORTICES