Short answer. The illegitimate children are entitled to one-fourth of the estate, and that quarter is taken from the free portion rather than out of your own share. As legitimate parent you keep the legitime the law reserves to ascendants, which is one-half of the estate.
What the law says
Illegitimate children who may survive with legitimate parents or ascendants of the deceased shall be entitled to one-fourth of the hereditary estate to be taken from the portion at the free disposal of the testator.
Civil Code, Article 896 — Illegitimate Children With Ascendants. Read the full provision →
Where the quarter comes from matters
The important words are to be taken from the portion at the free disposal of the testator. The illegitimate children's quarter is not carved out of the ascendants' legitime; it is carved out of the half your son was otherwise free to give away by will. So in the ordinary case the estate divides into a half reserved to the legitimate parents or ascendants, a quarter reserved to the illegitimate children, and a remaining quarter still free. That last quarter can be left to anyone — including to the same children, or to a partner. If your son left no will disposing of it, the free portion does not simply vanish; it passes under the rules on intestate succession.
How this article reads today
The fraction here was framed on the classification of children used when the Civil Code took effect in 1950, and the article must be read subject to the Family Code. The Family Code provides that the legitime of each illegitimate child is one-half of the legitime of a legitimate child, and that "except for this modification, all other provisions in the Civil Code governing successional rights shall remain in force." The Family Code also recognises a single class of illegitimate child, so the older sub-classifications the Civil Code used no longer separate one illegitimate child from another. All of your son's illegitimate children share the reserved quarter equally, whatever the circumstances of each birth.
Who is displaced, and who is not
Parents and ascendants inherit as compulsory heirs only where the deceased left no legitimate children or other legitimate descendants. A single surviving legitimate child would displace you from this position entirely, and the shares would be computed under a different rule. A surviving spouse does not displace you but takes a legitime of her own out of the same estate, which reduces what remains free. Note also that this article governs the legitime — the minimum the law reserves. It does not stop your son from having given the free portion to his children by will, and it does not decide how his debts and estate taxes, which come off the top, are paid.
What to settle before dividing anything
Two facts drive the whole computation, so establish them first: whether each claimant child's filiation to your son can be proved, and whether he left a will. Filiation is shown by the birth certificate the parent signed or participated in, a written acknowledgment, an admission in a public or private document, or open and continuous possession of the status of a child. Then take an honest inventory of assets and liabilities at the date of death. Estate tax deadlines run from that date whether or not the family agrees. Avoid signing an extrajudicial settlement that assumes shares nobody has computed; if the children's status is disputed, book a consultation first.