  Known Majorana fermions models are considered as promising ones for the
purposes of quantum computing robust to decoherence. One of the most expecting
but unachieved goals is an effective control for braiding of Majoranas. Another
one is to describe ${\mathbb{Z}}_2$ topological semimetals, APRES spectra of
which testify on eight-fold degenerate chiral fermions with $SU(2)$ holonomy of
wave functions, whereas the last can not be reproduced within existing models.
Quasi-relativistic theory of non-abelian quantum charge transport in
topological semimetals is developed for a model with a number of flavors equal
three. Majorana-like quasi-particle excitations in the model are described with
accounting of dynamic mass term arising due to relativistic exchange
interactions. Such exotic features of $\mathbb{Z}_2$ semimetals as splitting
zero-conductance peaks, longitudinal magnetoresistance, minimal direct current
conductivity, negative differential conductivity have been calculated in
perfect agreement with experimental data. We propose a new scheme of braiding
for three flavor Majorana-like fermions with new non-trivial braiding operator.
We demonstrate that in this model, the presence of chiral Majorana-like bound
states is controlled as emergence of three pairs of resonance-antiresonance in
frequency dependence of dielectric permeability.
