This study introduces a novel fluxgate current sensor with a compact, ring-shaped configuration that exhibits improved performance through the integration of magnetization residence times and neural networks. The sensor distinguishes itself with a unique magnetization profile, denoted as M waves, which emerge from the interaction between the target signal and ambient magnetic interference, effectively enhancing interference suppression. These M waves highlight the non-linear coupling between the magnetic field and magnetization residence times. Detection of these residence times is accomplished using full-wave rectification circuits and a Schmitt trigger, with a digital output provided by timing sequence detection. A dual-layer feedforward neural network deciphers the target signal, exploiting this non-linear relationship. The sensor achieves a linearity error of $0.054\%$ within a measurement range of 15 A. When juxtaposed with conventional sensors utilizing the residence-time difference strategy, our sensor reduces linearity error by more than 40-fold and extends the effective measurement range by $150\%$. Furthermore, it demonstrates a significant decrease in ambient magnetic interference.