On transverse-universality of twist knots

In the search for transverse-universal knots in the standard contact structure on ${\mathbb{S}}^3$, we present a classification of the transverse twist knots with maximal self-linking number, that admit only overtwisted contact branched covers. As a direct consequence, we obtain an infinite family of transverse knots in $({\mathbb{S}}^3,{\xi }_{std})$ that are not transverse-universal, although they are universal in the topological sense.