Can you claim a child on your taxes if the child receives public assistants?

Only if all of the rules are met by you and the child that receives the public assistance for you qualify to be able claim the qualifying dependency exemption on your 1040 income tax return for this purpose.

For all of the rules go to the IRS gov website and use the search box for PUBLICATION 17 go to chapter 3. Personal Exemptions and Dependents

Each test is explained in chapter 3 of the publication 17 and you will also find the worksheet that you can use to determine if the support test is met.