  Magnetic and topological properties along with quantum correlations in terms
of several entanglement measures have been investigated for an
antiferromagnetic spin-1/2 XY model in the presence of transverse magnetic
field and XZX$-$YZY type of three-spin interactions. Symmetries of the spin
Hamiltonian have been identified. Under the Jordan-Wigner transformation, the
spin Hamiltonian converted into spinless superconducting model with nearest
neighbor hopping and Cooper pairing terms in addition to next nearest neighbor
Cooper pairing potential. Long range antiferromagnetic order has been studied
in terms of staggered spin-spin correlation functions, while the topological
orders have been characterized by winding numbers. Magnetic and topological
phase diagrams have been prepared. Faithful coexistence of magnetic and
topological superconducting phases is found in the entire parameter regime.
Boundaries of various quantum phases have been marked and positions of
bicritical points have been identified.
