Er sitzt an einem kleinen Tisch.

Note

Now he finished the process of sitting down, he is situated at the table. We are no longer talking about the direction of a movement but about the location, where the man is at.

an einem kleinen Tisch

is Dative

When we want to describe a location, we use prepositions followed by a dative.

in einem Café

an einem Tisch

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How do German cases work?
German has four grammatical cases: nominative (subject), accusative (direct object), dative (indirect object), and genitive (possession). The case determines the form of articles and adjectives. For example, "the dog" is "der Hund" as a subject but "den Hund" as a direct object.

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