  We systematically studied the transport properties of single crystals of
$Eu_{1-x}Sr_xFe_{2-y}$Co$_{y}As_2$. Co doping can suppress the spin-density
wave (SDW) ordering and induces a superconducting transition, but a resistivity
reentrance due to the antiferromagnetic ordering of $Eu^{2+}$ spins is
observed, indicating the competition between antiferromagnetism (AFM) and
superconductivity. It is striking that the resistivity reentrance can be
completely suppressed by external magnetic field (H) because a metamagnetic
transition from antiferromagnetism to ferromagnetism for $Eu^{2+}$ spins is
induced by magnetic field. Superconductivity without resistivity reentrance
shows up by partial substitution of Eu$^{2+}$ with non-magnetic Sr$^{2+}$ to
completely destroy the AFM ordering of $Eu^{2+}$ spins. These results suggest
that the antiferromagnetism destroys the superconductivity, while the
ferromagnetism can coexist with the superconductivity in the iron-based
high-$T_c$ superconductors.
