  In this paper, we study in the context of quantum vertex algebras a certain
Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW
type and classify its $\mathbb N$-graded irreducible modules by using a notion
of Verma module. On the other hand, we introduce a new algebra, a twin of the
original algebra. Using this new algebra we construct a quantum vertex algebra
and we associate $\mathbb N$-graded modules for Jing-Nie's Clifford-like
algebra with $\phi$-coordinated modules for the quantum vertex algebra. We also
show that the adjoint module for the quantum vertex algebra is irreducible.
