If he is the father you should put him on the birth certificate for your child's sake. It won't affect parenting time. He will probably get parenting time. You can request the home is looked at to be sure it is safe for the child.
Please be advised my answers to questions does not constitute legal advise and you should not rely on it, due to the fact that we have never met, I have not been aprised of the facts in you case nor have I reviewed any documents.
I agree with Ms. Navarette's answer. The father is usually given parenting time for the sake of the child, but you can make all attempts necessary to make sure the visits are safe for the child, especially since your description of the father doesn't make him seem like the most responsible person.
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The name of the child's natural father should appear on the birth certificate. How much parenting time he gets is a complex issue that is too complicated to address in this forum. For example, if he doesn't seek any formal parenting time he will not have any (as parenting time schedules are not automatically set). If he makes an application for parenting time, ultimately, the court is guided by what is in the child's "best interest."
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