It depends on your state. Texas just today passed a new law allowing this, so you need to check your state laws. Everyday they seem to change.
You can only "amend" a paternity affidavit if you have a paternity test done to prove or disprove paternity... In many cases this is something that the state will do (ie of child support orders)
Laws vary in different jurisdictions. Generally, an unmarried father who signed an affidavit of paternity has established his paternity and can file a custody case. If you were never married to the other parent of your child, and never signed an affidavit of paternity then you must establish paternity legally (by a DNA test) before you can start a custody case.
Send the alleged father a letter via certified mail, return receipt requested, asking that he submit to a paternity test. If he refuses, you will have to file a paternity lawsuit, where the court will order him to take a paternity test. If you must file a lawsuit, you should see a family law attorney.
If the couple are unmarried the birth mother is presumed to have full custodial rights to the child.. The assumed father is not automatically granted any rights to a child until paternity is established either by the signing of the birth certificate or affidavit of parentage or a paternity test. When parentage has been established the biological father can file a writ of habeas corpus for custoday or a petition for visitation rights; likewise the primary custodial parent can then petition for child support.
Are you requesting a paternity test to determine if you're the father, or chasing down a father? If you're the man, see link.
She can get away with it until you go to court and file a motion for a court ordered paternity test. If the test disproves your paternity, you can file a motion to cease child support based on that.
The short answer is yes. The affidavit simply establishes a presumption of paternity. The father has no actual rights (to custody, parenting time, or support) until he files a paternity suit. If he did file a paternity suit, no DNA test will be required, and he will be found to be the father, because he is on the affidavit. Next, the court would issue an Order of Filiation. At that point, the mother would be bound by Michigan's 100 mile rule, and would not be able to more more than 100 miles from the other parent unless given permission by the court. However, in your case, all you have is an affidavit of parentage. You can move out of state without permission of the other parent or the court.
If your ex-girlfriend is refusing to have a paternity test done, you do have other means of getting one. You would have to file a court petition, with a compelling statement of why a paternity test would be reasonable.
By "sign the birth certificate" I assume you mean, signed a voluntary acknowledgment of paternity. That establishes paternity. Paying child support does not establish paternity. But, if you're paying child support and later learn you're not the father, you cannot stop paying under any circumstances in 20 states, and had a two year limit to file in the other 30, even if the mother has married the biological father. Always get a paternity test before signing a birth certificate. see links
A paternity test can determine if there is a parent-child relationship between two people. A paternity test would give genetic proof of that relationship.
You will need to file a paternity lawsuit in court. The court will then order that a paternity test be done to determine whether you are the father of the child. I strongly recommend that you talk with a family law attorney before filing a lawsuit. A listing of family law attorneys is available in your local phonebook.
see link below "Can you have a paternity test while you are pregnant?"