  We analyze condensation behaviors of neutral scalar fields outside
horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was
known that minimally coupled neutral scalar fields cannot exist outside
horizonless reflecting stars. In this work, we consider non-minimal couplings
between scalar fields and Maxwell fields, which is included to aim to trigger
formations of scalar hairs. We analytically demonstrate that there is no hair
theorem for small coupling parameters below a bound. For large coupling
parameters above the bound, we numerically obtain regular scalar hairy
configurations supported by horizonless reflecting stars.
