abseits
away from
Used as a preposition with the genitive to express spatial distance or separation from something.
Wir machten ein Picknick abseits der lauten Straße.
We had a picnic away from the noisy road.

offside / away
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away from
Used as a preposition with the genitive to express spatial distance or separation from something.
Wir machten ein Picknick abseits der lauten Straße.
We had a picnic away from the noisy road.

The word 'abseits' (away from/off to the side) derives from 'ab' (away) and 'Seite' (side). So it literally describes a position that is away from the side or from the center.
Das Haus liegt etwas abseits, mitten im Wald.
The house is located somewhat out of the way, in the middle of the forest.
'Abseits' (away from/off to the side) can be used as a preposition with a noun or as a stand-alone adverb. As a preposition, it introduces a location; as an adverb, it describes a position without a direct object.
Wir saßen abseits des Trubels auf einer Parkbank.
We sat on a park bench away from the hustle and bustle.
When 'abseits' (away from) is used as a preposition, it requires the genitive. In colloquial speech, the dative with 'von' is sometimes used incorrectly, but in written language the genitive is correct.
Ihr Ferienhaus liegt abseits der großen Touristenorte.
Their holiday home is located away from the major tourist resorts.
there / with you
'dabei' and 'abseits' form a contrast here. 'dabei' means that someone is present at an event or with a group, or is taking part. 'abseits' means that someone is not directly involved in the main action or is standing some distance away. So 'dabei' fits when someone is part of the situation. 'abseits' fits when someone tends to stay separate from the others or is not really taking part.

Sofia steht auf der Feier abseits und spricht mit niemandem.
Sofia is standing off to the side at the party and is not talking to anyone.
Am Samstag ist der neue Gast beim Ausflug dabei.
On Saturday, the new guest is coming along on the outing.