Looks like 15 or so times

He pitched in the first inning 714 times, and in the fourth inning 699 times. There is likely some noise that keeps it from being as simple as 714-699, such as entering a game early in relief. But I would think somewhere between 12-18 would be a pretty safe bet. Pretty rare I think, but a bit higher than I would have guessed.

For reference, a few others
Maddux 740 first innings, 728 fourths, difference of 12
Carlton 709, 693, 16
Nolan Ryan 774, 731, 43
Fergie 594, 576, 18

Click here for link at https://www.baseball-reference.com/players/split.fcgi?id=nie