Two people claimed to be his children. One is Carlo Meucci, said to have been born on February 3, 1872 in New York. This is unlikely as Esther would have been in her 60s. The other is Esther Mathilda Nisini Grosch, who was born at Antonio's home. She claimed that her mother told her she was Antonio's illegitimate daughter.
Have you taken a DNA test for genealogy? If so, login to add it. If not, see our friends at Ancestry DNA.