verweisen auf
to refer to
To point something out or direct attention to something; to refer to something.
Der Autor verweist in der Fußnote auf eine weiterführende Studie.
The author refers in the footnote to a further study.

to refer / expel
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to refer to
To point something out or direct attention to something; to refer to something.
Der Autor verweist in der Fußnote auf eine weiterführende Studie.
The author refers in the footnote to a further study.

'Verweisen' (to refer/expel) is an inseparable verb based on the basic verb 'weisen' (to point/show). The prefix 'ver-' directs the action of pointing toward something else or away from a place.
Der Professor verwies auf die Wichtigkeit der Quellenangaben.
The professor referred to the importance of citing sources.
When pointing to a source, a piece of information, or a connection, the fixed structure is always 'verweisen auf' + accusative. This phrase is typical of academic and formal texts.
Für weitere Details verweise ich auf das Handbuch.
For further details, I refer you to the manual.
To exclude someone from a place, there are two constructions. The very formal variant uses the genitive: 'jemanden des Landes verweisen' (to expel someone from the country). More common is the variant with 'aus' + dative: 'jemanden aus dem Raum verweisen' (to expel someone from the room).
Der Spieler wurde nach der roten Karte des Feldes verwiesen.
The player was sent off the field after the red card.
When sending a person to another place for help or information, you use the structure 'jemanden an' + accusative. The person being sent away is also in the accusative.
Der Arzt verwies mich an einen Spezialisten.
The doctor referred me to a specialist.
The phrase 'jemanden auf die Plätze verweisen' (to relegate someone to the lower places) is a fixed idiom and is used almost exclusively in sports reporting. It means that an athlete was better than their competitors.
Die Schwimmerin verwies ihre Konkurrenz auf die Plätze zwei und drei.
The swimmer relegated her competition to second and third place.
to fly
'fliegen' and 'verweisen' can both mean that someone has to leave a school or another institution. 'fliegen' is colloquial and often short for 'hinausgeworfen werden' (to be thrown out / kicked out). For example, you can say: 'Er ist von der Schule geflogen.' (He got kicked out of school.) 'verweisen' sounds official and usually needs an object: a school expels someone from the school. Learners may confuse the words because the situation is similar. Remember: 'fliegen' colloquially describes what happens to the person; 'verweisen' describes the official decision.

Die Schulleitung hat den Schüler nach dem Vorfall von der Schule verwiesen.
After the incident, the school administration expelled the student from the school.
Wegen der vielen Fehlstunden ist er fast von der Ausbildung geflogen.
Because of his many absences, he almost got kicked out of the training program.