  The generation of squeezed Fock states by the one or more photon subtraction
from a two-mode entangled Gaussian (TMEG) state is theoretically addressed. We
showed that an arbitrary order Fock state can be generated this way and we
obtained a condition that should be imposed on the parameters of the TMEG state
to guaranty such a generation. We called the regime, in which this condition is
satisfied, universal solution regime. We showed that, for first squeezed Fock
state, the above condition is redundant such that the generation of the first
squeezed Fock state is still possible by a one photon subtraction from an
arbitrary TMEG state. At the same time, the maximum generation probability of
the first squeezed Fock state generation corresponds to the universal solution
regime. We applied the above results to the description of generation of the
squeezed Fock states using a beam splitter and a Controlled-Z operation. We
have estimated the parameters of such setups and input squeezed states, which
are necessary to obtain squeezed Fock states with the maximum probability.
