The same as any father's. He just needs to go to court to get them .
The question is: Does the lover may prevail over the cuckold?
Except as provided in Section 7541, the child of a wife cohabiting with her husband, who is not impotent or sterile, is conclusively presumed to be a child of the marriage.
(a)Notwithstanding Section 7540, if the court finds that the conclusions of all the experts, as disclosed by the evidence based on blood tests performed pursuant to Chapter 2 (commencing with Section 7550), are that the husband is not the father of the child, the question of paternity of the husband shall be resolved accordingly.
(b)The notice of motion for blood tests under this section may be filed not later than two years from the child's date of birth by the husband, or for the purposes of establishing paternity by the presumed father or the child through or by the child's guardian ad litem. As used in this subdivision, "presumed father" has the meaning given in Sections 7611 and 7612.
(c)The notice of motion for blood tests under this section may be filed by the mother of the child not later than two years from the child's date of birth if the child's biological father has filed an affidavit with the court acknowledging paternity of the child.
(d)The notice of motion for blood tests pursuant to this section shall be supported by a declaration under oath submitted by the moving party stating the factual basis for placing the issue of paternity before the court.
Thus, according to Ca laws third parties CANNOT contest paternity of marital children.