Girl observing purdah in front of an illegitimate son of her father

If he is born from your mother and father before they entered into wedlock, then he is your mahram. Hence, purdah is not compulsory between you and him.

However, if he is an illegitimate child of your father born from another woman, then since there is a possibility of him being your father's child, there is also the possibility of him being the child of another man as other men could have had relations with the woman, therefore in this case, you should make purdah from the illegitimate son of your father born from another woman.

And Allah Ta'ala (الله تعالى) knows best.