There is a code snippet to set the UILocalNotification to fire at every sunday 20:00.
NSCalendar *calendar = [[NSCalendar alloc] initWithCalendarIdentifier:NSGregorianCalendar];
NSDate *now = [NSDate date];
NSDateComponents *componentsForFireDate = [calendar components:(NSYearCalendarUnit | NSWeekCalendarUnit| NSHourCalendarUnit | NSMinuteCalendarUnit| NSSecondCalendarUnit | NSWeekdayCalendarUnit) fromDate: now];
[componentsForFireDate setWeekday: 1] ; //for fixing Sunday
[componentsForFireDate setHour: 20] ; //for fixing 8PM hour
[componentsForFireDate setMinute:0] ;
[componentsForFireDate setSecond:0] ;
NSDate *fireDateOfNotification = [calendar dateFromComponents: componentsForFireDate];
UILocalNotification *notification = [[UILocalNotification alloc] init] ;
notification.fireDate = fireDateOfNotification ;
notification.timeZone = [NSTimeZone localTimeZone] ;
notification.alertBody = [NSString stringWithFormat: @"New updates!"] ;
notification.userInfo= [NSDictionary dictionaryWithObject:[NSString stringWithFormat:@"New updates added for that week!"] forKey:@"new"];
notification.repeatInterval= NSWeekCalendarUnit ;
notification.soundName=UILocalNotificationDefaultSoundName;
NSLog(@"notification: %@",notification);
[[UIApplication sharedApplication] scheduleLocalNotification:notification] ;
enjoy