Castle airs on Saturdays and Sundays in most markets on local broadcast channels, like ABC. It’s usually late at night if not overnight into Monday morning. The show is not exclusively airing on ABC stations as it could be airing on your Fox, CW, or CBS affiliate station.
The show also airs on TNT. But it is an infrequent schedule and is usually overnights on Mondays or Tuesdays and Fridays or Saturdays. It seems as though TNT just throws it in wherever. TNT schedule updates will be posted as a “post” basis on the main website at www.castleseries.net.
The show is also available on iTunes and Amazon either by episode or you can buy the season.