My Wife, and 14 month Daughter is living with me in California and are on H4 Visa. Since they do not have a SSN , can I still claim my child for 'Child Tax Credit'. I am filling under Married Filling Jointly.

Also Is there any other way I can get Tax Credits for my Daughter other than exemptions ? She was never sent to daycare.

I do not think so.

You need to get Individual Tax Identification Numbers (ITINs) for your wife and child.

Unfortunately, the ITINs (which begin with a 9) are coded to identify people who are NOT eligible for the Child Tax Credit or Earned Income Credit.