geringfügig
minor
Very small, insignificant, or negligible in extent, degree, or importance.
Der Preis wurde nur geringfügig erhöht.
The price was increased only slightly.

minor
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minor
Very small, insignificant, or negligible in extent, degree, or importance.
Der Preis wurde nur geringfügig erhöht.
The price was increased only slightly.

This meaning is very specific and is used almost only in a work context. It describes 'geringfügige Beschäftigung' (marginal employment), also called a 'Minijob', where you remain below a certain income limit.
Viele Studenten arbeiten nebenbei geringfügig.
Many students work part-time in marginal employment.
As an adverb, 'geringfügig' (slightly) modifies a verb and means 'a little' or 'slightly'. In this function, the word is not declined and often stands directly before the past participle or adjective it describes.
Die Pläne wurden nur geringfügig geändert.
The plans were changed only slightly.
The word is based on the adjective 'gering' (small/low), which means 'klein' (small) or 'wenig' (little). Something that is 'geringfügig' (minor) therefore has only a small, insignificant effect or size.
Es gibt nur einen geringfügigen Unterschied zwischen den beiden Modellen.
There is only a minor difference between the two models.
'Geringfügig' (minor/slight) belongs more to written language or a more formal style. In normal conversation, people would often simply say 'ein bisschen' (a little), 'etwas' (somewhat), or 'kaum' (hardly).
Der Schaden am Auto war zum Glück nur geringfügig.
Fortunately, the damage to the car was only minor.
something / somewhat
'etwas' and 'geringfügig' can both express that a difference or change is small. 'etwas' is very common in everyday language and can mean 'a little' before adjectives or verbs. 'geringfügig' sounds more precise and more factual; it fits well when you want to say that something is only very slight or hardly important. In everyday life, people often say 'etwas teurer' (somewhat more expensive) or 'etwas besser' (somewhat better). In reports, or when talking about prices or changes, 'geringfügig' often sounds more appropriate.

Die Miete steigt im nächsten Jahr nur geringfügig.
The rent will rise only slightly next year.
Vor dem Termin ist die Stimmung im Büro etwas angespannt.
Before the appointment, the mood in the office is somewhat tense.