TAMPA — Gerrit Cole didn’t get to enjoy the Yankees’ off day on Monday because he was feeling under the weather. No, there was nothing to be concerned about, coronavirus worriers.

The $324 million man was feeling better and back to work by Tuesday, so there was more teasing and more tutoring for one of the Yankees’ comers who figures to be a rotation mate for Cole by 2021 or 2022, if not sooner.

This superstar to super prospect mentoring has been one of the best parts of Clarke Schmidt’s first big-league spring training.

After Schmidt’s outing on Tuesday at Steinbrenner Field, a one-run, two-inning, three-strikeout effort in the Yankees’ 9-1 win over the Boston Red Sox, it was class in session again.

Cole studied Schmidt’s outing from start to finish from the Yankees dugout, then they went to the clubhouse to talk pitching while standing with a baseball in their right hand.

This Schmidt start began in the fourth inning with Red Sox third baseman Rafael Devers homering on a first-pitch fastball, then six of the next eight Red Sox hitters were retired. The outing impressively ended with Andrew Benintendi, one of baseball’s best young hitters, whiffing at a nasty changeup.

“He thought my stuff was really good and we were talking about how with the four-seam (fastball) they were kind of ambushing a little bit and ways we can get them off of it in the season,” said Schmidt, who is ranked the Yankees’ No. 2 prospect by MLB Pipeline. “He had really good takeaways and really good tips. A lot of the stuff was finger pressures on different pitches. We were talking about changeups.

“Every time I talk to him it’s very detail oriented, very methodical. Everything he has to say is so deep thought, so every time I’m talking to him, I’m learning something. And we’ve got to talk a good bit here this spring. He’s been really good to me.”

The teasing also has been fun for Schmidt, a 24-year-old from suburban Atlanta who was the Yankees’ top draft pick in 2017.

Even though Schmidt hasn’t pitched beyond Double-A - he had just four starts with Trenton late last season – he feels like one of the Yankees big leaguers when he’s teased by Cole about some of his quirky habits.

“He’s always picking on me,” Schmidt said with a smile. “It’s small stuff. We’ll be stretching and Gerrit is always sure to find me and give me a little banter here and there. But it’s good though. There are worse people to be making fun of me!”

They might be teammates for real starting this year because Schmidt has been so impressive this spring that he’s in the running to begin the season in the Yankees’ rotation as a fill-in starter for James Paxton, who is due to return from back surgery in May or June.

Schmidt has looked like a legit contender allowing just one run over five innings in three outings this spring, but he’ll probably begin the season back in the minors because 2020 is just his second full season as a pro due to him being drafted out as a college junior at South Carolina early into recovering from Tommy John surgery.

“I do know I kind of have the cards stacked against me because I’m not on the 40-man (roster) and Paxton is coming back within a month or so, but I try not to put too much pressure or thought into it,” Schmidt said. “I just want to go out there and impress. There’s no bad thing with me whether I win the job or not. I’m not losing sleep over it. I know that I’m learning a lot here being around these guys and I’m facing major league hitters.”

Schmidt isn’t just facing major league hitters. He’s retiring a lot of them, and making some of them look bad in the process with a curveball that Yankees manager Aaron Boone calls “special.”

Whenever Schmidt’s big-league ready, he can partially credit Cole for speeding up his timeframe.

“He’s kind of taken me until his wing a little bit and given me a lot of tips,” Schmidt said. “And he’s got the good banter, too, so it’s a lot of fun.”

Randy Miller may be reached at rmiller@njadvancemedia.com. Follow him on Twitter @RandyJMiller. Find NJ.com on Facebook.