Can I be sued for back child support?

Was told more than 20 years ago that a child was mine. I offered to pay child suupport but the mom left the state with any line of communication. I have recently contacted my possible daughter and we have discussed a DNA test to confirm whether or not I am truly her father. She is now 21 and I am concerned that her mother will sue my for back support. Are there any limitations to this? I want to r