Illegitimate children shall use the surname and shall be under the parental authority of their mother, and shall be entitled to support in conformity with this Code. However, illegitimate children may use the surname of their father if their filiation has been expressly recognized by the father through the record of birth appearing in the civil register, or when an admission in a public document or private handwritten instrument is made by the father. Provided, the father has the right to institute an action before the regular courts to prove non-filiation during his lifetime. The legitime of each illegitimate child shall consist of one-half of the legitime of a legitimate child.