The investigation of orthodox [Formula: see text]-restriction semigroups was initiated by Jones in 2014 as generalizations of orthodox [Formula: see text]-semigroups. The aim of this paper is to further study orthodox [Formula: see text]-restriction semigroups based on the known results of Jones. After establishing a construction theorem for orthodox [Formula: see text]-restriction semigroups, we introduce proper [Formula: see text]-restriction semigroups (which are necessarily orthodox) and prove that every (finite) orthodox [Formula: see text]-restriction semigroup has a (finite) proper cover. Our results enrich and extend existing results for restriction semigroups and orthodox [Formula: see text]-semigroups.