Superconducting and topological states are two quantum phenomena attracting much interest. Their coexistence may lead to topological superconductivity sought-after for Majorana-based quantum computing. However, there is no causal relationship between the two, since superconductivity is a many-body effect due to electron-electron interaction while topology is a single-particle manifestation of electron band structure. Here, we demonstrate a novel form of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing, induced by topological Weyl nodal lines in Ising Bardeen-Cooper-Schrieffer (IBCS) superconductors. Based on first-principles calculations and analyses, we predict that the nonmagnetic metals of MA$_2$Z$_4$ family, including ${alpha}_1$-TaSi$_2$P$_4$, ${alpha}_1$-TaSi$_2$N$_4$, ${alpha}_1$-NbSi$_2$P$_4$, ${alpha}_2$-TaGe$_2$P$_4$, and ${alpha}_2$-NbGe$_2$P$_4$ monolayers, are all superconductors. While the intrinsic IBCS paring arises in these non-centrosymmetric systems, the extrinsic FFLO pairing is revealed to be evoked by the Weyl nodal lines under magnetic field, facilitating the formation of Cooper pairs with nonzero momentum in their vicinity. Moreover, we show that the IBCS pairing alone will enhance the in-plane critical field $B_c$ to ~10-50 times of Pauli paramagnetic limit $B_p$, and additional FFLO pairing can further triple the $B_c/B_p$ ratio. It therefore affords an effective approach to enhance the robustness of superconductivity. Also, the topology induced superconductivity renders naturally the possible existence of topological superconducting state.
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