Zorder in plots with different x-axis in matplotlib

You can set the order using ax.set_zorder(ax3.get_zorder()+1); ax.patch.set_visible(False) which will help bring the blue line in front.

import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots(figsize=(10, 6))

ax3 = ax.twiny()
ax3.errorbar([1, 2, 3, 4], [1, 2, 3, 4], yerr = [1, 2, 3, 4], fmt='o', color='gray', zorder = 1)
ax3.plot([-1,4], [1,2], c = 'black', zorder = 2)
ax3.tick_params(axis='x')
ax3.tick_params(axis='x', colors='gray')
ax3.set_xlim(-1,4)

ax.tick_params(axis='x')
ax.tick_params(axis='x', colors='mediumblue')
ax.grid(color='grey', linestyle='-', linewidth=0.5, zorder = 1)
ax.errorbar([1.1, 2.1, 3.1, 4.1, 2.91], [1.1, 2.1, 3.1, 4.1,2], yerr = [1.1, 2.1, 3.1, 4.1,1], fmt='o', color='mediumblue', zorder = 4, capsize=0.1)

ax.grid(axis='y')
ax.set_zorder(ax3.get_zorder()+1)
ax.patch.set_visible(False)

plt.tight_layout()
plt.show()