A sukka built under a balcony, even if the balcony is many stories above the sukka, is not kosher.

Situation

Only part of a sukka is under the balcony.

Status

To be kosher, the sukka must have a footprint at least 7 by 7 tefachim and must have at least three walls that are not under the balcony.

Note If you have only two walls with the overhanging balcony, consult a rabbi.