We introduce the periplectic q-Brauer category over an integral domain of characteristic not 2. This is a strict monoidal supercategory and can be considered as a q-analogue of the periplectic Brauer category in [18]. We prove that the periplectic q-Brauer category admits a split triangular decomposition in the sense of [6]. When the ground ring is an algebraically closed field, the category of locally finite-dimensional right modules for the periplectic q-Brauer category is an upper finite fully stratified category in the sense of [6]. We prove that periplectic q-Brauer algebras defined in [1] are isomorphic to endomorphism algebras in the periplectic q-Brauer category. Furthermore, a periplectic q-Brauer algebra is a standardly based algebra in the sense of [13]. We construct a Jucys-Murphy basis for any standard module of the periplectic q-Brauer algebra with respect to a family of commutative elements called Jucys-Murphy elements. Via them, we classify blocks for both the periplectic q-Brauer category and periplectic q-Brauer algebras in the generic case. Our result shows that both the periplectic q-Brauer category and periplectic q-Brauer algebras are always not semisimple over any algebraically closed field.