herausgeben
to hand over
To hand something that one owns or is holding over to another person, often in response to a request or demand.
Der Dieb wurde gezwungen, das gestohlene Geld herauszugeben.
The thief was forced to hand over the stolen money.

to hand over / publish / give change
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to hand over
To hand something that one owns or is holding over to another person, often in response to a request or demand.
Der Dieb wurde gezwungen, das gestohlene Geld herauszugeben.
The thief was forced to hand over the stolen money.

'Herausgeben' (to hand over / publish / give change) is a separable verb. The prefix 'heraus' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Verkäufer gibt mir das Wechselgeld heraus.
The salesperson gives me the change.
The verb consists of the directional particle 'heraus' (out of something toward the speaker) and the verb 'geben' (to give). Its literal meaning is therefore 'to give outward'.
Bitte gib den Ball aus dem Haus heraus.
Please give the ball out of the house.
In the meaning 'aushändigen' (to hand over), 'herausgeben' is often used in the context of a demand or compulsion. Typical objects are things that someone is hiding or does not give up voluntarily.
Die Polizei forderte den Verdächtigen auf, seine Waffe herauszugeben.
The police ordered the suspect to hand over his weapon.
When it is about publishing, the objects are typically media such as 'ein Buch' (a book), 'eine Zeitschrift' (a magazine), 'ein Album' (an album), or 'ein Magazin' (a magazine). The person who does this is 'der Herausgeber' (the publisher/editor).
Nächstes Jahr gibt die Band ihr neues Album heraus.
Next year, the band is publishing its new album.
To ask for change, you use the fixed structure 'auf [Betrag] herausgeben' (to give change for [amount]). The verb often appears in a question with 'können' (can).
Entschuldigung, können Sie auf einen 20-Euro-Schein herausgeben?
Excuse me, can you give change for a 20-euro bill?
to publish
'veröffentlichen' and 'herausgeben' can both mean that a book, magazine, or other medium becomes available to the public. 'veröffentlichen' is more general and also fits articles, music, films, or information on the internet. 'herausgeben' is used especially for books, magazines, newspapers, or collections; it often sounds like a person or organization is organizing and publishing the content. The words can be confused because they are often very close in meaning with media. If you mean making something public in general, 'veröffentlichen' is a safe choice. If you are talking about a book, magazine, or edition, 'herausgeben' often sounds natural.

Die Schule gibt jedes Jahr eine kleine Zeitung heraus.
The school puts out a small newspaper every year.
Er veröffentlicht regelmäßig kurze Texte auf seinem Blog.
He regularly publishes short texts on his blog.