die Aussetzung
abandonment
Leaving behind a person in need of help or an animal in a place where they cannot help themselves.
Die Aussetzung von Haustieren im Wald ist eine Straftat.
The abandonment of pets in the forest is a criminal offense.

abandonment / suspension / reward
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abandonment
Leaving behind a person in need of help or an animal in a place where they cannot help themselves.
Die Aussetzung von Haustieren im Wald ist eine Straftat.
The abandonment of pets in the forest is a criminal offense.

'Aussetzung' is a noun derived from the separable verb 'aussetzen' (to abandon; to suspend). The ending '-ung' turns the verb into a feminine noun and describes the action or result of 'Aussetzen' (abandoning or suspending).
Die Aussetzung des Hundes war herzlos.
The abandonment of the dog was heartless.
The three meanings are very different. The context reveals what is meant: if it is about animals or helpless people, it means being left behind. In a legal or formal text, it usually means 'Unterbrechung' (interruption/suspension). If it is about money for information, it means a reward.
Die Firma beantragte eine Aussetzung der Zahlungen.
The company applied for a suspension of payments.
In the meaning 'Zurücklassen' (leaving behind/abandonment), the word is often used in legal or formal contexts. It is a term from criminal law and animal protection law.
Die Aussetzung eines Kindes ist eine schwere Straftat.
The abandonment of a child is a serious criminal offense.
In the meaning 'Unterbrechung' (interruption/suspension), 'Aussetzung' is often used with a genitive that indicates what is being interrupted. Typical phrases are 'Aussetzung des Verfahrens' (suspension of the proceedings), 'Aussetzung der Strafe' (suspension of the sentence), or 'Aussetzung der Vollstreckung' (suspension of enforcement).
Der Anwalt beantragte die Aussetzung des Verfahrens aus gesundheitlichen Gründen.
The lawyer applied for the suspension of the proceedings for health reasons.
reward
'die Belohnung' and 'die Aussetzung' can be connected in one special case: money promised for finding something or capturing a person. 'Belohnung' directly names the money or prize. 'Aussetzung' in this context refers more to the public offer of such a reward and sounds more formal. Learners may confuse the words because you can speak of 'die Aussetzung einer Belohnung' (the offering of a reward). In everyday language, however, 'Belohnung' is much easier to understand. 'Aussetzung' should only be used this way in suitable, rather official texts.

Die Polizei informierte die Presse über die Aussetzung einer hohen Belohnung.
The police informed the press about the offering of a large reward.
Für Hinweise zu dem gestohlenen Fahrrad gibt es eine Belohnung.
There is a reward for information about the stolen bicycle.