This paper introduces a method for online conformal prediction with decaying step sizes, which provides simultaneous guarantees for both adversarial and independent and identically distributed (I.I.D.) data sequences. Unlike previous methods, it can estimate a population quantile when it exists. The method achieves a long-run coverage guarantee for adversarial data and a convergence guarantee for I.I.D. data. Theoretical analysis shows that with decaying step sizes, the coverage approaches the desired level for every time point in the adversarial case, and converges to the desired level in the I.I.D. case. Experiments on real-world data, including the Elec2 and Imagenet datasets, demonstrate that decaying step sizes lead to more stable and accurate prediction sets compared to fixed step sizes. The method also allows for adaptive step size adjustments in response to distribution shifts, improving performance in dynamic environments. The results show that decaying step sizes provide better coverage and stability, making the method suitable for a wide range of online prediction tasks.This paper introduces a method for online conformal prediction with decaying step sizes, which provides simultaneous guarantees for both adversarial and independent and identically distributed (I.I.D.) data sequences. Unlike previous methods, it can estimate a population quantile when it exists. The method achieves a long-run coverage guarantee for adversarial data and a convergence guarantee for I.I.D. data. Theoretical analysis shows that with decaying step sizes, the coverage approaches the desired level for every time point in the adversarial case, and converges to the desired level in the I.I.D. case. Experiments on real-world data, including the Elec2 and Imagenet datasets, demonstrate that decaying step sizes lead to more stable and accurate prediction sets compared to fixed step sizes. The method also allows for adaptive step size adjustments in response to distribution shifts, improving performance in dynamic environments. The results show that decaying step sizes provide better coverage and stability, making the method suitable for a wide range of online prediction tasks.