Can a mother ask for child support from the father without him being on the birth certificate? What if the child turns 18 in less than 1 year?

You will want to get a paternity test before you agree to anythng.  If you are the biological father and there is no father in a court order and no father listed on the birth certificate, the mother may pursue the child support even this long after the child was born.  If mom was married at the time she had the child, then that husband is the presumed father of the child, and different time limits are involved.  An attorney could help you understand your rights and options in this situation.   It is fair to bring up that the mother has denied you an opportunity to know your child and should not be rewarded with back pay.  Especially if she knew where you were the whole time.  That may not be sufficient to prevent the court from ordering that you pay child support to mom until the daughter is age 18 and graduated from high school, whichever occurs last.  She has the right to seek retroactive child support.  There is a presumption in the law that four years of retroactive support is the maximum that may be ordered, but the court does not have to stick to that.  They will order a lump sum that is the total of the prior years' support added up and then order you to make installment payments toward the arrearage until it is paid off.  That arrearage will bear interest at the rate of six percent per year.  So, as you see, having an attorney by your side is very important.