s there anyway to get my child US citizenship without the fathers cooperation?

It is difficult unless he is a citizen by birth but you need to get certain documents and it would be difficult without his help.

*Derivative Citizenship* In some cases, people are U.S. Citizens and do not know it. In this case, it is possible for us to file what is known as a Derivative Citizenship Petition. It is a petition that if approved, will give proof of U.S. Citizenship. There is a significant amount of evidence that would be required for this type of petition, but if done properly, there is a reasonable chance of success. There are ways of obtaining records without his help.

In regard to adjudicating US Citizenship based on birth out of wedlock to a US Citizen father, you must have "legitimation" (legalizing the status of an illegitimate child) or, in lieu of legitimation, an acknowledgement of paternity in writing and under oath by the father or establishment of paternity by adjudication of a competent court in either Poland or the US prior to your child having reached the age of 18. [Ref. New Section 309(a) of the INA].

If your child was born out of wedlock (no marriage) after November 14, 1986, she can apply for proof of her citizenship if she can establish the following about her father: 1. That he is a US citizen at the time of your child's birth, 2. That he was physically present in the US for 5 years after his birth (two of which was after the age of 14), and 3. That he legitimated or accepted the child before she turned 18.

You need to hire a family attorney to establish that the father is the father. Then you may be able to apply for the child's citizenship without the father's signature.

Problem with the case is as you say, the acquisition of US citizenship upon the birth of your child abroad would depend (usually) on establishing the parent's physical presence in the US for a period of time before the child's birth. And without the cooperation of the parent that can be difficult. The answer to your question is that you do not need the parent's cooperation. However, finding the documentation which would establish the physical presence can be problematic without that cooperation. I know that this answer places you between a rock and a hard place, but these cases require evidence and without the evidence to support the claim of acquisition of US citizenship, the claim will often fail. Wish I could give you a better answer. Perhaps hiring a private investigator in the US to find available records may be helpful, but this will have a cost and of course no promise that the investigative services will lead to anything. Good luck.