Fortification enhancement

I was wondering as how the fortification enhancement works, my DM said he only believes that the light enhancement can be put on light armor, moderate enhancement on medium armor, and the heavy enhancement in heavy armor. He said he is unsure and I can’t find a really much on it

Ask them where they are reading that, because that's not listed anywhere.

Any armor can have any level of fortification

Like Name Violation says, light, moderate, or heavy fortification can be placed on any armor; light, medium, heavy, or any type of shield, even bucklers or tower shields.

The level of enchantment will work just effectively on any type.