Can I claim my dependents on my taxes this year even if I do not work. But I received family leave.

What do you mean by "claim dependents?"   You can enter dependents on a tax return, but if you do not have income earned from working, you are not eligible to receive refundable child-related credits like earned income credit or the additional child tax credit.  Those credits are based on having income from working.

You can always claim a dependent on your tax return if they meet the qualifications.  However, you won't get the child tax credit or the additional child tax credit unless you have income earned from working, or have substantial other income so that you owe tax.