You need to sit down with a lawyer ASAP. There is no prohibition on an illegal alien receiving custody or visitation in Georgia, but a judge may certainly consider the implications of that status, as well as other factors in custody. Adultery does not normally determine custody unless it had an effect on the child.
But let me stress that your post here on the internet is public and he can read it and so can his lawyer, and it was very unwise to admit to adultery in a public posting. At this point, you need to stay quiet online, and see a lawyer ASAP to protect your rights and represent you properly.
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