der Zeitgenosse
contemporary
A person who lives or lived in the same historical era as another person.
Goethe und Napoleon waren Zeitgenossen.
Goethe and Napoleon were contemporaries.

contemporary
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contemporary
A person who lives or lived in the same historical era as another person.
Goethe und Napoleon waren Zeitgenossen.
Goethe and Napoleon were contemporaries.

The word is made up of 'Zeit' (time) and 'Genosse' (comrade, companion). A 'Zeitgenosse' is therefore literally a 'companion in time'.
Als Zeitgenossen erlebten sie dieselben historischen Ereignisse.
As contemporaries, they experienced the same historical events.
'Zeitgenosse' is a noun of the N-declension. This means it takes the ending '-n' in all cases except the nominative singular.
Ich habe einen Artikel über einen Zeitgenossen von Mozart gelesen.
I read an article about a contemporary of Mozart.
The adjective 'zeitgenössisch' (contemporary) is derived from 'Zeitgenosse' (contemporary). It means 'originating from the same time' or 'modern'.
Die Ausstellung zeigt zeitgenössische Kunst aus Berlin.
The exhibition shows contemporary art from Berlin.
In the meaning of 'fellow human being' or 'person', 'Zeitgenosse' is almost always used with an adjective that characterizes the person. It often sounds slightly distant or formal.
Er gilt als ein sehr kritischer Zeitgenosse.
He is considered a very critical person.
person
'die Person' and 'der Zeitgenosse' can both refer to a human being. 'die Person' is the neutral word for an individual person. 'der Zeitgenosse' is more specific: it can be someone who lives or lived in the same time period as another person. It is also used for a person of the present day, often with a description such as 'ein netter Zeitgenosse' (a nice person / fellow) or 'ein schwieriger Zeitgenosse' (a difficult person / fellow). 'Person' fits almost always in a neutral way; 'Zeitgenosse' sounds more characterizing and somewhat elevated or humorous.

Unser neuer Nachbar ist ein freundlicher Zeitgenosse und grüßt jeden im Haus.
Our new neighbor is a friendly fellow and greets everyone in the building.
Am Telefon wollte meine Kollegin wissen, welche Person den Termin gebucht hat.
On the phone, my colleague wanted to know which person had booked the appointment.