Should I claim 0 or 1 withholding on my W-4 if I am single, full time college student, parents claim on taxes, and have one part-time job making less than $1000/year?

Do you have any scholarships that pay for non qualified expenses such as room and board? They would be taxable in addition to your part-time job income.

I have scholarships but none that pay for non qualified expenses.  Thank you for your help.

With the part time job for less than $1000 per year as your only taxable income, you could claim 1 for withholding or you could actually claim "exempt" since you will owe no taxes.