I had conviction (shoplifiting)19 years ago but was recorded as misdemeanor, its still showing on my criminal background check and now I cannot qualify for the Notary license, any suggestions how to clean this mess??

You may go back to court with an attorney and try to get it explunged.
That is assuming your state allows that.

If you have no other convictions you should qualify. Hire an attorney. Also this could take up to6 months ormore to accomplish so I hope you are not in a big hurry.