I live in Ohio and I have two young children. I was never married to the father and when we split up we filed for 50/50 custody. Then he stopped taking them half the time so I filed for primary custody and allowing visitation for him on the weekends. He agreed to that and it was filed, however child support still has not been established yet. Now he says that he can't pay child support because he got married and had another baby and he can't afford it. He also says that he did some research and thinks that he can sign his rights over to his mother so he doesn't have to pay child support. Can he do that? Do I have to allow that? What would that mean for her?

Did you read this (https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html)?

No he can't do that, and if he tried you don't have to allow it.

But really who cares, he is merely trying to lie and trick you into not going after child support.

You keep going after your support, his new wife and child means nothing it is a percent of his income that your child gets,/

Can his mother adopt the children? Will that release him of his child support? Would that make her obligated to pay child support?

Can his mother adopt the children? Will that release him of his child support? Would that make her obligated to pay child support?

Simple answer-NO!
3107.011 Arranging adoptions.

(A) A person seeking to adopt a minor shall utilize an agency or attorney to arrange the adoption. Only an agency or attorney may arrange an adoption.
3107.06 Consent to adoption.

Unless consent is not required under section 3107.07 of the Revised Code, a petition to adopt a minor may be granted only if written consent to the adoption has been executed by all of the following:

(A) The mother of the minor;

(B) The father of the minor, if any of the following apply:

(1) The minor was conceived or born while the father was married to the mother;

(2) The minor is his child by adoption;