USCIS may doubt the validity of his marriage if they are apprised that he had a child with another woman. I do not know if you filing for child support would necessarily trigger this inquiry, but he is required to disclose all children (regardless of their immigration status) to USCIS. His failure to do can be deemed a material misrepresentation which in turn can result in a permanent bar to admission. If he does not have an immigration attorney, he would be best advised to consult an attorney about the matter.
Your child is entitled to child support. As for his immigration process, it is quite complicated. If his marriage was not in good faith, then he will not be able to obtain his adjustment of status. Contact experienced family lawyer to assist you with the family law related issues.
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Child support is a separate issue from Immigration. if it's his baby he will still have to pay. As to his marriage to someone else, he will have to show it is bona fide...
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Child support application is a separate issue from his immigration application. The question is whether he had formally entered into divorce with you before marrying the other US citizen. If he had a formal divorce with you before his second marriage, it should not affect his immigration application. The USCIs may question about it but it is not going to be a problem if he can show a genuine marriage with his second wife.
I have dealt with a lot of I-130 application, quite a lot of beneficiaries have married two or three times.
USCIS may question the bona fide nature of his marriage but it is still possible for him to obtain his residence
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