Depends.  If you lived with your boyfriend for the ENTIRE year and you earned less than $4,150 and living together did not violate local law then yes he can claim you.

However, he can only claim your child if your child also lived with him for the ENTIRE year (if there is joint custody, he can't claim your child since your child would not have lived with him the entire year) AND if you did not work.  In order to claim someone, they cannot be a qualifying child of another taxpayer.  If you worked and file a tax return, your child would be your qualifying child so your boyfriend would not be able to claim them.

https://apps.irs.gov/app/vita/content/globalmedia/table_2_dependency_exemption_relative_4012.pdf