This paper considers a qubit interacting time-dependently with parametric converter
two-mode cavity fields. The dynamics of quantum effects, population inversion and
quantum coherence, have been investigated when the cavity fields start from entangled coherent states. The qubit starts from a superposition state. We have examined the effects of the difference between the two-mode photon numbers, the qubit time-dependent location, and the initial qubit state on the dynamics of the generated quantum coherence. It is found that the dynamics of the population inversion, the entropies, and the negativity qubit-cavity entanglement can be controlled by the difference between the two-mode photon numbers, the qubit location parameter as well as the initial qubit state.