zufälligerweise
coincidentally
Happening by chance; without intention or planning.
Ich habe zufälligerweise meinen alten Schulfreund im Supermarkt getroffen.
I coincidentally ran into my old school friend at the supermarket.

coincidentally
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coincidentally
Happening by chance; without intention or planning.
Ich habe zufälligerweise meinen alten Schulfreund im Supermarkt getroffen.
I coincidentally ran into my old school friend at the supermarket.

The word is built from 'zufällig' (random/by chance) and the ending '-erweise'. The ending '-erweise' is added to adjectives to form an adverb that describes a particular manner or circumstance.
Er hat dummerweise seinen Schlüssel vergessen.
Unfortunately, he forgot his key.
As an adverb, 'zufälligerweise' (coincidentally) can stand in different positions in the sentence. If it is in position 1, the conjugated verb follows directly. It can also stand in the middle of the sentence.
Zufälligerweise hatte ich meinen Regenschirm dabei.
Coincidentally, I had my umbrella with me.
The form 'zufälligerweise' (coincidentally) is often used to especially emphasize the chance nature of an event. It can sound somewhat more formal or narrative.
Ich wollte gerade das Haus verlassen, als zufälligerweise das Telefon klingelte.
I was just about to leave the house when, coincidentally, the phone rang.
conscious / deliberate
'bewusst' and 'zufälligerweise' are opposites when it comes to intention. 'bewusst' describes an action that someone does deliberately. 'zufälligerweise' describes something happening without planning. Also, 'bewusst' is an adjective or used adverbially, while 'zufälligerweise' is an adverb. If someone plans something or does it deliberately, 'bewusst' fits. If something happens only by chance, 'zufälligerweise' is correct.

In der Bibliothek traf Julian zufälligerweise seinen alten Lehrer.
In the library, Julian coincidentally ran into his old teacher.
Johanna kauft bewusst weniger Süßigkeiten, weil sie gesünder leben möchte.
Johanna deliberately buys fewer sweets because she wants to live more healthily.