I am sorry to hear that you are in this situation. You really need to consult with a family law attorney, as well as an immigration attorney. The two attorneys will need to work together to develpe a strategy for you so that you can get divorce, get custody of your child, and remain in the country.
Judges are required to consider incidents of domestic violence in the home when deciding which parent should be awarded custody in a divorce proceeding. OCGA 19-9-3. If you are fighting regularly, however, and especially if the fighting is happening in front of your child, then you and your husband are BOTH at risk of losing custody of your child.
You really have an immigration question here, which is, how does a police report affect your immigration status. I don't practice in that area, but have changed your topic heading so that immigration attorneys will see your question.
I am not your attorney and we do not have an attorney-client relationship. This answer is based only on the information you provided; new facts not shared here could change the answer. Relying solely on the internet for legal information, while convenient, can have disastrous consequences.
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