Singapore does not register births that occurred overseas. If a child is born overseas, the parents should register the child’s birth and obtain the birth certificate from the foreign authorities in the country/place where the child is born.
For more information: Please refer here: https://www.ica.gov.sg/enter-depart/for-singapore-citizens/child-born-overseas
Upon obtaining the child’s overseas birth certificate, the Singapore citizen parent can submit the Singapore Citizenship application for the child using his/her Singpass account.
Please refer to Becoming a Singapore Citizen for more information.