Does severance delay my unemployment claim? - what worked for you?

I was offered severance of 13 weeks after being let go as a bank teller and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. I have a mortgage and need to plan. Who should I ask before signing?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.