This is the 16169th most frequent Russian word.
районные
"District" or "regional."
Here, 'районные' (district) is an adjective describing schools that pertain to or are located in specific administrative districts.
Районные школы обычно находятся рядом с жилыми кварталами.
District schools are usually located near residential areas.
In this case, 'районные' (district) refers to administrations at the district level within a governance structure.
В районные администрации поступают обращения от граждан.
Citizens' petitions are received by district administrations.
Here, 'районных' (district) modifies 'спортивных соревнованиях' (sports competitions), indicating that the events are organized within the district boundaries.