Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a Beta$(2-α, α)$-coalescent for $α\in (1,2)$. We prove in a setting of moderate selection that the fixation probability $π_N$ of the advantageous allele is asymptotically equal to $α^{1/(α-1)} s_N^{1/(α-1)} $ , where $s_N$ is the selection strength of the advantageous allele. Our proof uses duality with a suitable $Λ$-ancestral selection graph.