If I was fired from my job with no clear evidence because someone said I was sleep when I was not, do I have a case?

Unless you are part of a Union and have a grievance process, you probably have no legal remedies. In Pennsylvania, there is no right to a job. Lawsuits are typically  allowed and successful in discrimination cases. These include gender and/or sex, age, race, religous and weight discrimination. If you fell asleep secondary ti sickness or as a side effect of medication, you may be able to prove that to your employer/supervisor and get a second chance. Good luck.