The Bogoliubov quasiparticle combines the properties of a negatively charged electron and a positively charged hole, so here we have two fermion and the quasiparticle have an integer spin. By this reason we have to consider this quasiparticle as boson, but in literature I came across with definition this one as fermion.Please, can anybody explain me what's wrong?
Bogoliubov transformation has a fermion version $+$ and a boson verion $-$.
The transformation is parameterized by $u$ and $v$ $$a=uc+vc^\dagger$$ $$a^\dagger=v^*c+u^*c$$
The goal is to restore similar commute relation as $c,c^\dagger$
The commutation relation determines the nature of fermion or boson.
Since you start with fermion, the Bogoliubov quasiparticle should also be fermion.
The "two" means a quantum superposition of two states, it does not mean you have two fermions particles.