You need to immediately retain a Custody attorney. You have rights, but you cannot just sit around and wait. You have to take action to protect those rights.
I am exclusively a family law attorney, practicing primarily in the metro Atlanta, Georgia trial courts. However, I handle appeals from anywhere in Georgia.
It appears, from the information you provided, that you were never married to the mother of your children and that you never legitimated them. It also sounds as if your children's mother has gotten married and her husband is now attempting to adopt the children. If this is the case, you do have the right to inform the court that you do not want your rights terminated, and let them know why.
I would strongly suggest that you contact a family law attorney in the area where your children life to get assistance with attempting to keep your parental rights.
I hope this helps with answering your question.
The above answer is a general explanation of legal rights and procedures. It does not constitute legal advice. Nor does it establish an attorney-client relationship between the individual posting the question and the attorney providing the answer.
Your question is about your consitutionally protected right to have a relationship with your children. But if you don't exercise it, such as by failing to see or contact them and failing to support them financially, you may lose it. The only way to test if you have kept your rights is to immediately file an action to legitimate them in the same court the action involving mom's asking to terminate your rights. You need a lawyer.
This answer is based on a very incomplete version of the facts. A complete and accurate answer is only available if a lawyer knows all the relevant history and circumstances of the case.