In order for the mother to obtain child support from you, a petition to establish that you are the father would be required, which would include DNA testing to confirm that you are the father.
That action may be brought in the state you live in or any other state as long as there is proper jurisdiction.
Jurisdiction is a highly technical issue that will require a qualified family law attorney to review. Under federal and most states laws, the state the mother lives in may file the proceedings and provide the mother free legal assistance to obtain child support. Most states have provisions for assisting parents with free legal services to obtain child support.
If you are the father, child support will be determined under the law of the state that has jurisdiction and, generally, your child support obligation is independent of whether you exercise your rights to be involved with the child.
The mother can pursue the paternity and child support action at anytime in the future. So if you have no interest in being involved with the mother or the child, should the mother not pursue having you declared the father at birth, you would have no rights as to the custody or adoption of the child.
If you wish to be notified of any proposed adoption of the child so you can then determine if you are the father, you would need to register as the putative father upon the birth of the child to protect those rights.
Additional information on child support in Illinois (where I practice) and the putative father registry can be found at http://www.childsupportillinois.com/general/index.html and http://www.putativefather.org/index.aspx.
You should contact a mens divorce attorney, such as the divorce lawyers for men at Cordell & Cordell, to review the specific facts of your case and discuss your options.
Use the Child Support Calculator on DadsDivorce.com for an estimated amount of how much child support you should be paying.