  The magnetic field is shown to affect significantly non-equilibrium
quasiparticle (QP) distributions under conditions of inverse proximity effect
on the remarkable example of a single-electron hybrid turnstile. This effect
suppresses the gap in the superconducting leads in the vicinity of turnstile
junctions with a Coulomb blockaded island, thus, trapping hot QPs in this
region. Applied magnetic field creates additional QP traps in the form of
vortices or regions with reduced superconducting gap in the leads resulting in
release of QPs away from junctions. We present clear experimental evidence of
such interplay of the inverse proximity effect and a magnetic field revealing
itself in the superconducting gap enhancement in a magnetic field as well as in
significant improvement of the turnstile characteristics. The observed
interplay of the inverse proximity effect and external magnetic field, and its
theoretical explanation in the context of QP overheating are important for
various superconducting and hybrid nanoelectronic devices, which find
applications in quantum computation, photon detection and quantum metrology.
