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In this paper, we investigate the structure of highest weight modules overthe quantum queer superalgebra $U_q(q(n))$. The key ingredients are thetriangular decomposition of $U_q(q(n))$ and the classification of finitedimensional irreducible modules over quantum Clifford superalgebras. The mainresults we prove are the classical limit theorem and the complete reducibilitytheorem for $U_q(q(n))$-modules in the category $O_q^{\geq 0}$.

Highest weight modules over quantum queer Lie superalgebra U_q(q(n))