A fastening system for applying, over an opening and surrounding fascia of a structure, a covering material including either of a flexible or rigid outer reinforced extending perimeter within which is configured a plurality of receiving apertures. At least one elongated rail adapted to being secured to the fascia in extending fashion proximate the opening, each of the rails exhibiting a three dimensional cross sectional shape with a forwardly projecting support surface within which is configured an outwardly facing narrowed slot. A plurality of fasteners each include a planar shaped base installable through an accessible end location of each of the rails so as to be traversable along an interior channel defined in the rail. A further rotatable portion of each fastener projects from the insertable base through the outwardly facing slot and in order to be rotated from a first position aligning with and seating over perimeter defined receiving apertures of the covering material to a second position in order to affix the material.