Minecraft 1.20.1 Forge
Mod version 1.8.2

On the second picture I manually turned off 3D hat in the config, however this way without the helmet the 3D hat doesn't render (as expected) and it looks weird.

I assume it's either a nodded helmet that is smaller than vanilla, or you messed with the settings. Either way the solution is to turn the voxel size in the settings down to fit under the helmet.