If I received a ticket for possession of a gram of marijuana and I pay the ticket does this even stay on an employer background check?

Usually in Texas, suspects are arrested, not ticketed, for possession of marijuana. There is a recent procedure in Harris County bypassing the arrest involving only certain police agencies. "Paying" a "ticket" is a permanent conviction. Maybe you have a possession of paraphernalia, which is usually ticketed and is always in a lower court (either a municipal or Justice of the Peace court).