The wavefunction of the Cooper pair of the conventional BCS state is characterized by an evenparity (s-wave) spin-singlet state. An external magnetic field is well known to modify the wavefunction of the Cooper pair and to break the conventional BCS superconducting state. We find that the wavefunction of the modified Cooper pair contains a spin-triplet component with s-wave orbital symmetry. While the spin-triplet s-wave Cooper pair is forbidden owing to the fermion property, it is permitted in the generalized theoretical framework containing an odd-frequency dependence of the order parameter. We investigate this point on the basis of the self-consistent calculation in the Eliashberg theory and find that the odd-frequency order parameter coexists with the evenfrequency one. We also report how the physical properties are affected by the induced odd-frequency superconducting order parameter.