A Josephson junction may be driven through a transition where the superconducting condensate favors an odd over an even number of electrons. At this switch in the ground-state fermion parity, an Andreev bound state crosses through the Fermi level, producing a zero-mode that can be probed by a point contact to a grounded metal. We calculate the time-dependent charge transfer between superconductor and metal for a linear sweep through the transition. One single quasiparticle is exchanged with charge $Q$ depending on the coupling energies $gamma_1,gamma_2$ of the metal to the Majorana operators of the zero-mode. For a single-channel point contact, $Q$ equals the electron charge $e$ in the adiabatic limit of slow driving, while in the opposite quenched limit $Q=2esqrt{gamma_1gamma_2}/(gamma_1+gamma_2)$ varies between $0$ and $e$. This provides a method to produce single charge-neutral quasiparticles on demand.
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