TAMPA — Clarke Schmidt has 27 minor league games in his first two professional seasons, because he had Tommy John surgery a month before being taken by the Yankees in the first round of the 2017 draft out of South Carolina.

In those 27 games, the right-hander has worked 114 total innings and has placed himself in position to climb the ladder from the minors to the majors quickly.

Schmidt, 24, made his second big league spring training outing Thursday against the Rays at George M. Steinbrenner Field in a 7-1 Yankees victory and drew high praise from a scout sitting behind home plate.

“It was his [second] big league game and it’s spring training, but when you can throw the breaking ball behind in the count for strikes, you have a chance to be really good,’’ the scout said of Schmidt, who worked two scoreless innings, allowed two hits, struck out three and didn’t issue a walk. “You can see him as a keeper.’’

There are two openings in the Yankees’ rotation due to injuries to James Paxton and Luis Severino, but Schmidt is the longest of long shots to fill one of those spots simply because he has never pitched above Double-A and has made only three starts at that level.

“That is tough to say. He doesn’t have a lot of experience yet as a professional pitcher,’’ Aaron Boone said when asked how much minor league work Schmidt would require before getting into position for a jump to the majors. “He is clearly advanced for that lack of experience. He has got a lot of the intangible things as well as the raw stuff to move quickly.’’

Aaron Judge hit in the cage, but Boone didn’t know when the right fielder would hit outdoors for the first time since being shut down from that activity at the start of camp due to a right shoulder problem.

“I don’t know when he will be on the field yet. I don’t know his exact schedule through the weekend,’’ Boone said. “But he is doing well.’’

Judge threw from 120 feet.

J.A. Happ started and pitched three innings, and said he was satisfied with the outing and getting to 40 pitches, of which 30 were strikes.

“I’m excited to continue to get the pitch count up and see the reactions of [pitches],’’ Happ said.

Aroldis Chapman threw batting practice on Field No. 2 and will repeat the process, likely Sunday, before making his spring training debut, which could be Wednesday night at Steinbrenner Field against the Phillies.

Tyler Wade’s bid to be the utility infielder strengthened when he hit a two-run homer in the first inning. The left-handed-hitting Wade, who also can play the corner outfield spots, then watched Clint Frazier complete the second leg of back-to-back blasts. Wade also stole two bases.

Mike Ford has a chance to make the roster due to his left-handed bat the Yankees need to keep balanced. The first baseman homered in the eighth inning and has three hits in eight at-bats.

A game was completed in two hours and 18 minutes, which proved it can be done, even with eight runs and 16 hits.

Deivi Garcia, the Yankees’ top pitching prospect, makes his spring training debut Friday against the Braves in North Port, Fla. Garcia. The 20-year-old right-hander pitched at Single-A, Double-A and Triple-A last season.