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We define the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertexalgebra that is an appropriate noncommutative generalization of the vertexoperator superalgebra. We also illustrate an example that can be viewed as anoncommutative generalization of the free fermion vertex operator superalgebra.The example is bulit upon a universal half-integer-graded non-anti-commutativeFock space where a creation operator and an annihilation operator satisfy thefermionic anti-commutativity relation, while no relations exist among thecreation operators. The former feature allows us to define the normal ordering,while the latter feature allows us to describe interactions among the fermions.With respect to the normal ordering, Wick's theorem holds and leads to a proofof weak associativity and a closed formula of correlation functions.

Fermionic construction of the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra and its $\mathbb{Z}_2$-twisted module, I