Short answer. That is the offence in Article 356 of the Revised Penal Code — threatening to publish a libel, and offering to prevent its publication for a price. It is complete on the threat and the demand. Nothing has to be published, and you do not have to have paid anything.
What the law says
any person who threatens another to publish a libel concerning him or the parents, spouse, child, or other member of the family of the latter, or upon anyone who shall offer to prevent the publication of such libel for a compensation or money consideration
Revised Penal Code, Article 356 — Threatening To Publish A Libel. Read the full provision →
Two ways the article is broken
Article 356 catches two different people. The first is the one who threatens to publish a libel about you — and the article expressly extends the protection to a libel concerning your parents, spouse, child or other family member, so a threat aimed at your family is a threat against you for this purpose. The second is anyone who offers to prevent the publication for compensation or money consideration. That second limb reaches the intermediary, the fixer who did not make the threat himself but who arrives offering to make it go away for a fee. Both are punished under the same article.
The penalty, and the current peso figures
The penalty is arresto mayor, or a fine of forty thousand to four hundred thousand pesos, or both. Those amounts come from Republic Act No. 10951 (2017), which revised the fines and property values throughout the Revised Penal Code. Older reproductions still print the 1930 figures, which were a small fraction of these, so a lower amount quoted elsewhere is almost certainly out of date. Note what the article does not require: no publication, no payment, no proof that the material was actually defamatory in the sense a libel case would need. The demand backed by the threat is the wrong.
When the threat arrives online
Most of these demands now come by message, and that changes the landscape. Where the threatened material is defamatory and would be posted through a computer system, the cybercrime law provides a heavier penalty for the libel itself, and a threat made electronically may also engage other provisions of that law. If the material is an intimate image or video, separate statutes on photo and video voyeurism and on violence against women and their children apply, and they are considerably stronger than this article. If a child is involved, still stricter child-protection laws govern. Say at the outset what kind of material is being held over you.
What to do while it is happening
Preserve everything before you reply: full screenshots showing the account name, the thread and the timestamps, the phone number or profile used, and any account details given for payment. Do not delete the conversation, however much you want it gone — the demand itself is the evidence of the offence. Paying rarely ends it and usually invites a second demand. Threats of this kind also frequently accompany extortion under other provisions with heavier penalties, so the charge finally filed may not be this one. No result can be promised in advance; take the preserved material to counsel quickly rather than negotiating alone.