The non-classical states of light serve as a potential candidate for emerging quantum information process. A processing trend to enhance its scalability is to integrate multiple nonlinear processes with the dressed-state picture into a single device, and therefore, are useful for quantum computations. Here, a novel method is proposed to experimentally achieve the generation of coexisting two pairs of narrow-band biphotons by two four-wave mixing processes in a single hot rubidium vapor cell. Based on the photon-atom nonlinear interfaces, the generated biphotons exhibits genuine entanglement in time-energy. Meanwhile, the nonlinear susceptibility with the dressed-state picture decides the temporal correlation of the biphotons wave packet as a damped periodic Rabi oscillation, suggesting the property of the high-dimensional time-energy entangled state. Such a high-dimensional entangled state also is an efficient way to enhance information carrying capacity. By alternating two nonlinear susceptibilities in a single device, respectively, there exists a competition of the generation rate between such two pairs of biphotons. Moreover, both generated two pairs of biphotons that violate the Cauchy-Schwarz inequality and show their non-classical behavior.