No, if the child's mother is claiming him then there isn't anyway for you to claim him also. If you received a 1095-A, you'll have to enter that, but otherwise...no information is needed about your son.
If you have a 1095-B, a form titled Health Coverage, the IRS does NOT need any details from this form. You can keep any 1095-B forms you get from your health insurance company or the government agency that sponsors your plan for your records.
If you have a 1095-C, a form titled Employer-Provided Health Insurance Offer and Coverage the IRS does NOT need any details from this form. You can keep any 1095-C forms you get from your employer for your records.
