When you “call on” someone, you pay them a short visit. It is also possible to say “call upon”, but this is considered to be rather formal.
Example: The students called on the ailing Principal on Wednesday afternoon.
When a teacher “calls on” a student in class, she wants him to answer the question.
Example: “I don’t understand why she has to call on me all the time”.
The expression “call at” is normally used in relation to a place. You usually call at some place. When you call at some place, you visit the individual at his place – it could be the office, home, etc.
Example: “I called at his office on my way to the airport”.
The expression “call at” can also be used to mean “stop at”.
Example: According to the brochure, our ship will call at five ports.