Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q, s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q, s) entanglement for α ≥1. We also obtain a class of tighter polygamy relations in the β-th (0≤β ≤1) power of unified-(q, s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for theα-th (0≤α≤1) andβ-th (β≥1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.