  We study conformal twist field four-point functions on a $\mathbb Z_N$
orbifold. We examine in detail the case $N=3$ and analyze theories obtained by
replicated $N$-times a minimal model with central charge $c<1$. A fastly
convergent expansion of the twist field correlation function in terms of sphere
conformal blocks with central charge $Nc$ is obtained by exploiting covering
map techniques. We discuss extensive applications of the formalism to the
entanglement of two disjoint intervals in CFT, in particular we propose a
conformal block expansion for the partially transposed reduced density matrix.
Finally, we refine the bounds on the structure constants of unitary CFTs
determined previously by the genus two modular bootstrap.
