  The details of unconstrained Lagrangian formulations (being continuation of
earlier developed research for Bose particles in NPB 862 (2012) 270,
[arXiv:1110.5044[hep-th]], Phys. of Part. and Nucl. 43 (2012) 689,
[arXiv:1202.4710 [hep-th]]) are reviewed for Fermi particles propagated on an
arbitrary dimensional Minkowski space-time and described by the unitary
irreducible half-integer higher-spin representations of the Poincare group
subject to Young tableaux $Y(s_1,...,s_k)$ with $k$ rows. The procedure is
based on the construction of the Verma modules and finding auxiliary oscillator
realizations for the orthosymplectic $osp(1|2k)$ superalgebra which encodes the
second-class operator constraints subsystem in the HS symmetry superalgebra.
Applying of an universal BRST-BFV approach permit to reproduce gauge-invariant
Lagrangians with reducible gauge symmetries describing the free dynamics of
both massless and massive fermionic fields of any spin with appropriate number
of gauge and Stukelberg fields. The general construction possesses by the
obvious possibility to derive Lagrangians with only holonomic constraints.
