This paper presents a method to realize a tunable Kitaev chain using a short Josephson junction with Andreev bound states (ABS). The key idea is to use the superconducting phase difference across the junction as a tunable parameter to control the couplings between quantum dots. By adjusting the phase difference, the system can be tuned into a sweet spot where the superconducting and normal couplings are balanced, leading to the emergence of a pair of poor man's Majorana zero modes. The phase difference also influences the effective superconducting gap and the transparency of the Josephson junction, allowing for fine-tuning of the system's properties. The study shows that the relative amplitude of elastic cotunneling (ECT) and crossed Andreev reflection (CAR) couplings can be controlled by the phase difference. At a phase difference of π, the system exhibits a large excitation gap and robustness against phase fluctuations, making it an optimal sweet spot. The paper also demonstrates that the system can be tuned into the strong coupling regime without changing the dot-hybrid coupling strength, by adjusting the phase and junction asymmetry. The authors analyze the system using perturbation theory and exact diagonalization, showing that the CAR and ECT amplitudes depend on the phase difference and junction asymmetry. They find that the optimal sweet spot occurs when the phase is π and the junction is slightly asymmetric, leading to the most robust Majorana zero modes and the largest excitation gap. The results suggest that the superconducting phase difference can be used as a tunable knob to realize a Kitaev chain with high-quality Majorana excitations. The study proposes a new device platform for realizing Kitaev chains using a short Josephson junction and highlights the potential of using flux control as a tuning method for quantum-dot-based Kitaev chains. The findings open up new possibilities for creating and controlling Majorana zero modes in quantum dot systems, with potential applications in topological quantum computing.This paper presents a method to realize a tunable Kitaev chain using a short Josephson junction with Andreev bound states (ABS). The key idea is to use the superconducting phase difference across the junction as a tunable parameter to control the couplings between quantum dots. By adjusting the phase difference, the system can be tuned into a sweet spot where the superconducting and normal couplings are balanced, leading to the emergence of a pair of poor man's Majorana zero modes. The phase difference also influences the effective superconducting gap and the transparency of the Josephson junction, allowing for fine-tuning of the system's properties. The study shows that the relative amplitude of elastic cotunneling (ECT) and crossed Andreev reflection (CAR) couplings can be controlled by the phase difference. At a phase difference of π, the system exhibits a large excitation gap and robustness against phase fluctuations, making it an optimal sweet spot. The paper also demonstrates that the system can be tuned into the strong coupling regime without changing the dot-hybrid coupling strength, by adjusting the phase and junction asymmetry. The authors analyze the system using perturbation theory and exact diagonalization, showing that the CAR and ECT amplitudes depend on the phase difference and junction asymmetry. They find that the optimal sweet spot occurs when the phase is π and the junction is slightly asymmetric, leading to the most robust Majorana zero modes and the largest excitation gap. The results suggest that the superconducting phase difference can be used as a tunable knob to realize a Kitaev chain with high-quality Majorana excitations. The study proposes a new device platform for realizing Kitaev chains using a short Josephson junction and highlights the potential of using flux control as a tuning method for quantum-dot-based Kitaev chains. The findings open up new possibilities for creating and controlling Majorana zero modes in quantum dot systems, with potential applications in topological quantum computing.