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The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars.