Can a father from mexico who never signed birth certificates or financially supported his children for 10 years fight for them legally ?
yes. He would have to come to the United States to do so and file in the county of your location. He can file a Petition for Paternity and have DNA tests done to determine the parentage of the children. If he is proven to be the father, then you can Petition the court for back child support.
There are many avenues, seek out a family law attorney.
If he is dad he has rights. Consider demanding a DNA test.
He can file paperwork with the courts to establish his rights, yes.