can every shard have a god metal

[spook lover]

I have just finished misborn and I could be stupid, but can all shards have God metals. I ask this because I just found out odium and honor have God metals so can other shards have them. and also, how does a shard make a god metal.    

[Returned he/him]

I'm not sure how much of Mistborn you've read, so please be aware that there are spoilers below. I've put them in spoiler tags, but be careful if you haven't read them all yet.

They can and do! Sazed talks a little bit about it in one of the Mistborn epigraphs (I don't remember which offhand), but the godmetal is a solid physical manifestation of a Shard's power. We don't know much about how the godmetals get their specific properties, but they seem to be related to the natures of the Shards themselves:

Spoiler

Mason Wheeler

Harmonium is ettmetal... Its chemicals properties are sort of analogous to cesium. It explodes in contact with water. People are made out of water. You try to spike someone, you try to swallow it, you try to wear it as jewelry, it will not end well. Why in the world would he pick something so inharmonious?

Brandon Sanderson

He didn't pick it. It's unstable because of the two halves of him not meshing well.

Oathbringer release party (Nov. 13, 2017)

Spoiler

classicalkhlennium

Could a Shard like Harmony create new elemental metals, like harmonium, or is that unconscious--

Brandon Sanderson

So, unconscious isn't the right word, but a manifestation of his will being the same as manifestation of the laws of physics in the world, if that makes sense. It's not like a choice, it's not, like, not a choice either, to create others, it is theoretically possible, but what has happened is more in line with the laws of his realm.

Oathbringer San Diego signing (Nov. 14, 2017)

We do know that there is some flexibility in how much of a godmetal physically exists, though the specifics of how and why are unclear as well. They can choose for there to be more or less, but that's as much information as I'm aware of. This WoB was the closest I could find on the topic, but it's not 100% clear exactly what this means, in the context of creating more of a godmetal or somehow permitting a godmetal to exist:

Spoiler

Questioner

Could [Sazed] also bring back lerasium beads, if he wanted to?

Brandon Sanderson

It would be within his power to do so, yes.

Firefight Miami signing (Jan. 8, 2015)