RTC and Interval Timing

I apologize. I did not look at your code carefully enough. The cascaded if/else conditions are turning the relays back off.

Your latest formulation looks correct. but remove the semicolon on the first line and check the parenthesis.

if( ( minute >= 0 && minute <10 ) || (minute >= 30 && minute < 40 ) )
{
  digitalWrite ( Relay2, HIGH);
}
else
{
  digitalWrite ( Relay2, LOW);
}

You could also try

 // Sets fan interval
  if ( minute >= 0 && minute < 10 )
  {
    digitalWrite ( RELAY2, HIGH );
  }
  //else
 // {
 //   digitalWrite ( RELAY2, LOW );
 // }
else  if ( minute >= 30 && minute < 35 )
  {
    digitalWrite ( RELAY2, HIGH );
  }

  else
  {
    digitalWrite ( RELAY2, LOW );
  }