Your child may be a U.S. citizen by virtue of birth to a U.S. citizen parent, and if so, could apply for a Certificate of Citizenship to prove that status. Regarding your spouse, you may be able to succeed in "consular processing" for your spouse to be able to enter the U.S. and to become a Lawful Permanent Resident (get a "Green Card"), and after approximately three years your spouse then may be able to apply to become a naturalized U.S. citizen. There are many details not mentioned in your question that could have an impact upon this analysis and upon immigration-related options. There really is no substitute for you and your spouse to consult with an immigration attorney who, after learning all of the relevant facts, could advise about immigration eligibilities, options and strategies and who could then offer legal representation in the often quite complex application process.
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