Unemployment claim submitted Dec. 30 for 4 days I was out of work during Christmas. Claim processed after Jan. 1. Money paid out after Jan. 1. Claim for 2017 or 2018?

If the check for the Unemployment Compensation was dated January 2018, then you won't be taxed on the income until 2018.  

Accordingly, you should receive a 2018 Form 1099-G for the Unemployment Compensation you received which will be reported on next year's tax return.