I suppose they are composed of fermions, but I wouldn't say that since quarks can't exist by themselves. But basically yes, they are composed the of fermions the same way that He-4 atom is.
It is alot easier to not refer to them as fermions and just as quarks, since leptons are also fermions.
Basically:
Bosons (Integer spins):
Mesons, Force carriers (photons/gluons), any atom where the sum of the spins is 0 such as He-4.
Hadron (quark composed particle):
Mesons, Baryons etc.
Lepton (Fundamental Particles):
Electrons, neutrinos.
Baryon (n/2 integer spins, were n is odd, Hadrons):
Protons, Neutrons
Fermions (n/2 integer spins, where n is odd, obey Pauli's Exclusion principle):
Baryons, Leptons.