  We consider the possibility for the existence of the third family of compact
objects, considering the effect of strong magnetic fields inside the hybrid
stars. As a result, we demonstrate such new sequences of stable equilibrium
configurations for some hadronic equations of state. Through the analysis of
the adiabatic index inside stars, we find the conditions for appearing the
third family of compact objects, i.e., for hadronic stars without quarks, that
the maximum mass should be small, the central density for the maximum mass
should be also small, and the radius for the the maximum mass should be large.
Even for soft hadronic equations of state, the two solar-mass stars might
survive as the third family of compact objects, once quark matter with strong
magnetic field, such as $\sim {\cal O}(10^{19} {\rm G})$, is taken into
account. It might give a hint to solve the so-called hyperon puzzle in nuclear
physics.
