(a) Children born out of wedlock shall be capable of inheriting and transmitting inheritance on the part of their mother and father.

(b) Prior to the death of the father, paternity shall be established by:

(1) Acknowledgment that he is the child's father;

(2) Adjudication on the merits pursuant to the provisions of article twenty-four, chapter forty-eight of this code; or

(3) By order of a court of competent jurisdiction issued in another state.

(c) After the death of the father, paternity shall be established if, after a hearing on the merits, the court shall find, by clear and convincing evidence, that the man is the father of the child. The civil action shall be filed in the family court of the county where the administration of the decedent's estate has been filed or could be filed:

(1) Within six months of the date of the final order of the county commission admitting the decedent's will to probate or commencing intestate administration of the estate; or

(2) If none of the above apply, within six months from the date of decedent's death.

(d) Any putative child who at the time of the decedent's death is under the age of eighteen years, a convict or a mentally incapacitated person may file such civil action within six months after he or she becomes of age or the disability ceases.

(e) The provisions of this section do not apply where the putative child has been lawfully adopted by another man and stands to inherit property or assets through his adopted father.

(f) The provisions of this section do not apply where the father or putative father has expressly disinherited the child in a provision of his will.