I have been receiving unemployment Comp for 4 months now. I took a job with a company as "Part Time-Fill In as Needed". The employer reported to the State of Alabama that my hire date was 1 March 2006. I filed my claim for 4 MArch 2006 reporting that I had not worked and not received any pay from the company for that week (which is entirely true). I even sent in the time sheet and a lett from my employer stating that. Now the State has found that (and I don't know how) I owe that week's pay back. I am going to appeal it, but would like some Law that shows where I should not have to pay it back. Any ideas?

If you have a statement from your employer that you did not work during the week for which you received UI, present it at your appeal. I don't have a crystal ball here, but it appears pretty clear that you don't owe it back. The adjudicator should see that too.