  It was recently shown that a chiral topological phase emerges from the
coupling of two twisted monolayers of superconducting
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ for certain twist angles. In this work, we
reveal the behavior of such twisted superconducting bilayers with $d_{x^2-y^2}$
pairing symmetry in presence of applied magnetic field. Specifically, we show
that the emergent vortex matter can serve as smoking gun for detection of
topological superconductivity in such bilayers. Moreover, we report two
distinct skyrmionic states that characterize the chiral topological phase, and
provide full account of their experimental signatures and their evolution with
the twist angle.
