How do I go about getting a lawyer to get rights to my child?

What you will need to do is establish paternity. By having her ex sign the birth certificate, she is portraying that the child father is her ex not you. Which is why a partenity needs to be established. And once that is done, you need to get your name on the birth certificate and request equal rights such as a Joint-Custody with the child. You can expect to pay anywhere from $3,500 to $7,500 as fathers-rights are harder to enforce and not many attorneys specialize in fathers rights. Feel free to contact my office and speak with a case manager at 877-866-8665 or email help@smsattorneys.com as we do also offer reduced price services for PRO SE people who can't afford an attorney or would like to represent themselves in court.