nebenbei
on the side
In addition to a main activity; as a side activity.
Er studiert Vollzeit und arbeitet nebenbei in einem Café.
He studies full-time and works on the side in a café.

on the side / incidentally
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on the side
In addition to a main activity; as a side activity.
Er studiert Vollzeit und arbeitet nebenbei in einem Café.
He studies full-time and works on the side in a café.

'Nebenbei' is made up of the prepositions 'neben' (beside/next to) and 'bei' (by/at/with). Literally, it means 'alongside it' or 'in addition to it' and describes something that happens in parallel with another thing.
Sie lernt für ihre Prüfung und hört nebenbei Musik.
She studies for her exam and listens to music at the same time.
As an adverb, 'nebenbei' can stand flexibly in the sentence. If it stands in position 1, the conjugated verb follows immediately (inversion).
Er hat das nebenbei erledigt.
He took care of that on the side.
In this meaning, 'nebenbei' is often connected with activities that bring in extra money or knowledge. Typical phrases are 'nebenbei arbeiten' (to work on the side), 'nebenbei Geld verdienen' (to earn money on the side), or 'nebenbei eine Sprache lernen' (to learn a language on the side).
Viele Studenten müssen nebenbei arbeiten, um ihr Studium zu finanzieren.
Many students have to work on the side to finance their studies.
The expression 'nebenbei bemerkt' (incidentally/by the way) is a very common way to weave additional, less important information into a conversation.
Das Meeting war sehr produktiv. Nebenbei bemerkt, es gab auch sehr guten Kaffee.
The meeting was very productive. Incidentally, there was also very good coffee.
there / with you
'dabei' and 'nebenbei' can both show that something is happening at the same time as something else. 'dabei' directly connects two actions: while someone is doing something, something else happens or they do something else. 'nebenbei' is more likely to mean that something happens in addition to the main thing or is mentioned only in passing. It often sounds less important than the main activity. Learners may confuse the words because both have to do with simultaneity. As a simple rule: 'dabei' fits with 'währenddessen' (meanwhile / while doing so), while 'nebenbei' fits with 'zusätzlich' (in addition) or 'not as the main thing'.

Die Lehrerin arbeitet tagsüber in der Schule und lernt nebenbei für eine Prüfung.
The teacher works at the school during the day and studies for an exam on the side.
Mein Kollege kocht das Mittagessen und hört dabei Nachrichten.
My colleague is cooking lunch and listening to the news while doing so.