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Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums ofVirasoro Lie conformal algebra and its nontrivial conformal modules of rankone. In this paper, we give a complete classification of extensions of finiteirreducible conformal modules of $\mathcal{W}(a,b)$. With a similar method, wecharacterize all extensions of finite irreducible conformal modules ofSchr\"{o}dinger-Virasoro type Lie conformal algebras $TSV(a,b)$ and $TSV(c)$.

Extensions of finite irreducible modules of Lie conformal algebras $\mathcal{W}(a,b)$ and some Schr\"{o}dinger-Virasoro type Lie conformal algebras