  The existence of eV-mass sterile neutrinos is not ruled out because of
persistent experimental anomalies. Upcoming multi-messenger detections of
neutron-star merger remnants could provide indirect constraints on the
existence of these particles. We explore the active-sterile flavor conversion
phenomenology in a two-flavor scenario (1 active + 1 sterile species) as a
function of the sterile neutrino mixing parameters, neutrino emission angle
from the accretion torus, and temporal evolution of the merger remnant. The
torus geometry and the neutron richness of the remnant are responsible for the
occurrence of multiple resonant active-sterile conversions. The number of
resonances strongly depends on the neutrino emission direction above or inside
the remnant torus and leads to large production of sterile neutrinos (and no
antineutrinos) in the proximity of the polar axis as well as more sterile
antineutrinos than neutrinos in the equatorial region. As the black hole torus
evolves in time, the shallower baryon density is responsible for more adiabatic
flavor conversion, leading to larger regions of the mass-mixing parameter space
being affected by flavor mixing. Our findings imply that the production of
sterile states could have indirect implications on the disk cooling rate, its
outflows, and related electromagnetic observables which remain to be assessed.
