A while ago I tested positive positive for thc while I was in the military. I was investigated by cid but only got a company grade art 15. I was also finger printed by cid. My question is if I was to be finger printed for employment would any of this show up in the back ground check?

It's impossible to say definitely but I would say it would - it would appear that Article 15 is some sort of discipline?

Ok, first finger print is just that, finger print to prove ID, your "fingerprint" does not have any criminal record attached to it.

When a finger print check is done, it is merely to prove who you are, nothing more, nothing less.

Then they will take that ID, and run a real criminal background check.
Normally the article 15 do not show up in normal background searches. It is possible of course for them to run a check of military records.

What grade ART15 was it? Without knowing if it was a company level or a field grade, done by brigade for example, this question is can't be conclusively answered.