I was caught shoplifting when I was over 18. The amount that I shoplifted was a little over a $100. I was not take to court but I did pay a fine that of about 300 that was issued by a lawyer. I am have an internship that requires a background check and am wondering if it will show up?

No you did not pay a fine, you paid a civil penalty that the store got from you as black mail not to press charges.

So first stop using the term fine, they call it that to make you think you have a legal obligation to pay it.
It has nothing to do with a court fine.

And no, unless there were police, a court summons there is no criminal record of this.

If you ever run for office in a political race, there is some record that I am sure a reporter can find, but it is not a criminal record