Reporting part-time earnings while on benefits - first time posting

I picked up part-time shifts as a quality inspector and I am confused about how to report them. I am in Madison, in case local advice matters. Pay posts on a different day from when I work. Who can I ask without risking my claim?

Thanks for writing this out. I went through something close to it 8 months ago, and it settled down once I kept a simple log of every call and form.