Hello. My name is***** will be happy to answer your question.
I am sorry to hear about this unfortunate situation.
Please note, I cannot comment on your specific situation, as this services is only limited to general information and for any legal advice / legal service you should contact your local attorney.
Generally, in similar situation the father would have to file a Petition to Establish Child Custody / Visitation with the local family law court, which is local as to where the minor son and mother are located.
The immigration status is not an issue and is now considered when it comes to Child Custody / Visitation proceedings, however, the fact that someone is living illegally in the US can be brought up in court by the mother, if it is relevant to the father's ability to provide safe visitation / home environment for the minor child.
Child custody / visitation proceedings are legally complex, so it is important to consult and retain an experienced local child custody law attorney to represent you if you decide to pursue child custody / visitation through the courts.
You can find an experienced and skilled local child custody law attorney by using this established and reputable attorney information / referral websites:
When, choosing a local attorney to represent you, it would be a good idea to choose someone who has a practice exclusively dedicated to child cutody law, has at least 10 years of experience and handled similar matters and also regularly practices before the court located in the jurisdiction where your matter will be heard.
I wish you the best of luck!