"my newborn boy"
If the child is your biological child, then the rules are different from the qualifying relative rules mentioned in the other answer. Your own child can be your qualifying child dependent if they are a US citizen or permanent resident and have a social security number, and they live with you more than half the year (or more than half the time they were alive if born in 2016), and they don't earn half their own support (this is obviously very rare for children). The fact that support might be paid by the state is not part of the test for qualifying child. Residency is usually the main factor.
Your fiancee can't be a qualifying child relative but could be a qualifying relative dependent if they meet the tests is the other answer.
Certainly, failing to disclose your support puts your fiancee at risk of being accused of welfare fraud, and could cost a small fortune for benefits payback, legal fees, and maybe even jail or community service time. And your state may check state tax returns to see if there are any children receiving benefits who are listed as dependents on other people's tax returns. So you will want to think about that. But for IRS purposes, you can claim your child as a dependent if the child lives with you, regardless of benefits that the child or the mother might receive.
