  We study the Josephson effect in a clean noncentrosymmetric
superconductor/half-metal/noncentrosymmetric superconductor junction, which is
grown on the surface of a three-dimensional Topological Insulator (TI) in the
ballistic limit. We find the signature of anomalous Andreev Bound States (ABS)
and band splitting for a spin-active barrier whose barrier magnetic moment is
misaligned with the bulk moment. The chiral Majorana mode and 4$\pi$ periodic
ABS are found to exist on the surface of TI for parallel orientation of the
moments in the normal incidence condition. But for anti-parallel misalignment,
we observe the 2$\pi$ periodic ABS. There exist a gap in ABS for oblique
incidence. We find the splitting of Andreev levels in the presence of RSOC and
also for unequal mixing of singlet-triplet correlations present in NCSC. The
Majorana mode, ABS and Josephson supercurrent can be controlled by the ratio of
barrier magnetic and non-magnetic moments. The critical current is found to be
maximum for singlet or triplet dominated NCSC, while it is minimum in the equal
mixing condition. The ABS is found to be barrier thickness dependent and is
suppressed for an opaque barrier. We observe a monotonic decay in critical
current with a finite length of the junction for all the singlet-triplet
mixings and magnetic moments. The current-phase relation is found to be
sinusoidal with no phase shift in the half-metallic limit, however, for
different orientations of the bulk moment, an anomalous characteristic is also
observed.
