Short answer. On that combination the Civil Code gives the legitimate ascendants one-half of the inheritance, the surviving spouse one-fourth, and the illegitimate children the remaining one-fourth. So as his mother you take a half, his widow a quarter, and his illegitimate child a quarter of the net estate.
What the law says
the ascendants shall be entitled to one-half of the inheritance, and the other half shall be divided between the surviving spouse and the illegitimate children so that such widow or widower shall have one-fourth of the estate, and the illegitimate children the other fourth
Civil Code, Article 1000 — Ascendants, Spouse and Illegitimate Children. Read the full provision →
Read the old text with the Family Code correction
The shares in this article were worked out on the classification of children in use when the Code took effect in 1950. The Family Code has since changed that scheme. It provides that the legitime of each illegitimate child is one-half of the legitime of a legitimate child, and that except for that modification the Civil Code's provisions on successional rights remain in force. It also recognises a single class of illegitimate child, so the older sub-classifications — acknowledged natural children and the rest — no longer apply. Read this article subject to that rule. On your facts no legitimate child survives, so the one-half, one-fourth, one-fourth division still governs.
The quarter is shared, not multiplied
The article speaks of illegitimate children in the plural, and the fourth it assigns is a single block for all of them together. If your son left one illegitimate child, that child takes the whole quarter. If he left three, they divide that same quarter among themselves — the ascendants' half and the widow's fourth do not shrink to make room. The same logic runs the other way for ascendants: if both of his parents had survived, they would have divided the one-half between them rather than each taking a half. The fractions attach to classes of heirs, not to individual heads.
What the fractions are applied to
These are shares of the net hereditary estate, not of everything in your son's name. Two subtractions come first. If he was married under the absolute community or the conjugal partnership, the property regime has to be liquidated, and the surviving spouse's own half of the community or conjugal property is hers by right of ownership — it is not part of what is being inherited at all. Then the debts, taxes, funeral and administration expenses come off. Only the remainder is divided in the proportions above, which is why a widow's total often looks far larger than a quarter.
Filiation and the mechanics of settlement
The illegitimate child inherits only if filiation to your son is established — through the record of birth, an admission in a public document or a signed private handwritten instrument, or in the other ways the law allows. Where the child was never acknowledged, that is usually the real dispute rather than the arithmetic. If all the heirs agree and there are no debts, an estate may be settled extrajudicially in the manner the rules provide; if they do not agree, it goes to a judicial settlement. Estate tax obligations run in parallel. This page gives general information, not advice on your son's estate.