I have an unmarried child. Allow me to go to marriage, immigration and America. But the father column of the child's birth certificate is not biological.

It doesn't matter, just prove that it is your child;

On the contrary, if you don't bring your young children when you apply for marriage immigration, it is easy to be rejected by immigration officials, because they may think that you want to abandon your children and go to the United States to enjoy happiness alone, and they will reject your application.