  In this paper we address Lifshitz transition induced by applied external
magnetic field in a case of iron-based superconductors, in which a difference
between the Fermi level and the edges of the bands is relatively small. We
introduce and investigate a two-band model with intra-band pairing in the
relevant parameters regime to address a generic behaviour of a system with
hole-like and electron-like bands in external magnetic field. Our results show
that two Lifshitz transitions can develop in analysed systems and the first one
occurs in the superconducting phase and takes place at approximately constant
magnetic field. The chosen sets of the model parameters can describe
characteristic band structure of iron-based superconductors and thus the
obtained results can explain the experimental observations in FeSe and Co-doped
BaFe$_{2}$As$_{2}$ compounds.
