Texas has a 4 year limit to file for paternity here and back support.So if it has been more than 4 years and no paternity established they cannot sue you for this.
§ 160.204. PRESUMPTION OF PATERNITY.
(a) A man is presumed to be the father of a child if:
(1) he is married to the mother of the child and the child is born during the marriage;
(2) he is married to the mother of the child and the child is born before the 301st day after the date the marriage is terminated by death, annulment, declaration of invalidity, or divorce;
(3) he married the mother of the child before the birth of the child in apparent compliance with law, even if the attempted marriage is or could be declared invalid, and the child is born during the invalid marriage or before the 301st day after the date the marriage is terminated by death, annulment, declaration of invalidity, or divorce;
(4) he married the mother of the child after the birth of the child in apparent compliance with law, regardless of whether the marriage is or could be declared invalid, he voluntarily asserted his paternity of the child, and:
(A) the assertion is in a record filed with the bureau of vital statistics;
(B) he is voluntarily named as the child ’s father on the child ’s birth certificate; or
(C) he promised in a record to support the child as his own; or
(5) during the first two years of the child ’s life, he continuously resided in the household in which the child resided and he represented to others that the child was his own.
(b) A presumption of paternity established under this section may be rebutted only by:
(1) an adjudication under Subchapter G; or
(2) the filing of a valid denial of paternity by a presumed father in conjunction with the filing by another person of a valid acknowledgment of paternity as provided by Section 160.305.
§ 160.607. TIME LIMITATION: CHILD HAVING PRESUMED FATHER.
(a) Except as otherwise provided by Subsection (b), a proceeding brought by a presumed father, the mother, or another individual to adjudicate the parentage of a child having a presumed father shall be commenced not later than the fourth anniversary of the date of the birth of the child.