It's asking me for total amount received for public assistance/welfare for state modified gross income. I understand it's non taxable. Should it be left blank?

No, you should enter it.  Like the federal sales tax deduction, many calculations require the addition of nontaxable income to see if you qualify.

what is considered public assistance? all i receive snaps and medicaid...

medicaid isn't money so you don't need to include that.  If SNAPS are food stamps, you would include the value of those.