An exact generalization of the Ramsey transition probability is derived to improve ultrahigh precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The phase shift accumulated at the end of the interrogation scheme and associated with the particle wave function is offering a very high-level control of quantum states throughout various laser parameters conditions. The generalized hyper-Ramsey resonance based on independent manipulation of interaction time, field amplitude, phase, and frequency detuning is presented to increase performances in the next generation of atomic, molecular, and nuclear clocks, to upgrade high-resolution frequency measurement in Penning trap mass spectrometry and for a better control of light-induced frequency shifts in matter-wave interferometer or quantum information processing