I’m sure you could find more detailed stats, but theoretically 2nd and 4th quarters should be highest scoring.
2 and 4 have a hard stoppage of play after so there’s some real urgency to score before the quarter ends. Teams have the 2 minute warning, will use their timeouts, and hurry up play to score quicker. 1st and 3rd quarters don’t have a hard stop, so there’s no urgency to try and score before the quarter ends and drives will continue into the next Q.
This also means that you can start the 2nd and 4th quarters already in good scoring position which makes it more common to score early in the Q, where 1st and 3rd you almost always start at your own ~20.
And while 2 and 4 are similar in those regards, 4 has the disadvantage that the game can already be decided and the winning team will run out the clock and not try to score.