There are very limited opportunities to establish paternity after the death of a parent but it is possible to do so as long as the mother was not married at the time the child was born and no paternity has been previously established.
According the Florida Department of Heath, if a birth record contains an error it may be possible to correct the record depending on the type of correct and the age of resistant, documentary evidence may be required to support the correction.
Once the father has died it is still possible to establish paternity by one of the following
(a) The natural parents participated in a marriage ceremony before or after the birth of the person born out-of-wedlock, even though the attempted marriage is void.
(b) The paternity of the father is established by an adjudication before or after the death of the father. Chapter 95 shall not apply in determining heirs in a probate proceeding under this paragraph.
(c) The paternity of the father is acknowledged in writing by the father.
Acknowledgment in writing may be in the form of a birth certificate, affidavit, or other writing such as a beneficiary designation under a life insurance policy. There are no formalities that are required and one court refused to require such evidence. In re: Estate of Jerrido, 339 So.2d 237 (Fla. 4th DCA 1976) the court refused to require authenticated evidence.