BOSTON — Few expected Clarke Schmidt to be a regular in the Yankees’ rotation when spring training began this year, but there he was on Thursday night, making his 29th start of the season.

Michael King is getting a jump-start on making a bid to do the same next year.

King continued to make his case to get a shot at cracking the 2024 rotation, turning in another solid start on Thursday afternoon in the Yankees’ 5-0 loss to the Red Sox before they split the doubleheader with a 8-5 win in the nightcap at Fenway Park.

After King gave up one run across 4 ²/₃ innings in Game 1, Schmidt was not quite as effective in Game 2, allowing four runs (three earned) across 5 ¹/₃ innings.

But he got the offensive support that King did not, with Aaron Judge clubbing a grand slam, DJ LeMahieu hitting a go-ahead double and Oswald Peraza adding some late insurance with his first home run of the year.

By the end of another long day — their second split doubleheader in three days — the Yankees (74-73) had taken three of four games in the series and left Boston tied with the Red Sox (74-73) for fourth place in the AL East.

While King was not as efficient Thursday as he had been recently — still on a pitch count as he builds up a starter’s workload — he struck out eight while scattering six hits and a walk.

Over his past five starts, he has given up just three earned runs across 21 ¹/₃ innings (1.27 ERA) with 29 strikeouts and four walks.

Depending on what moves the Yankees make this offseason, King could have a shot to continue starting next season.

“Probably technically to be determined, but I think we all believe he could be a starter,” manager Aaron Boone said. “I think he’s probably, in a lot of ways, confirming that in what we’re seeing as he continues to build up here these last few weeks.

“We’ll see where the next few weeks take us. We’ll see where the winter takes us and how we look going into next season. But right now, he’s putting himself in that starter mix.”

By his next start, King should have close to a normal allotment of pitches at his disposal.

With three starts left, he is in line to surpass 100 innings on the season, an important step if he takes on a starting role next season.

Schmidt is also in uncharted territory in terms of his workload, finishing Thursday with a career-high 146 innings and 4.56 ERA.

The Yankees have given him extra days in between starts when possible, but believe he has responded well.

“I think he feels really good,” Boone said. “He’s still very strong, pitching very well. … No plans to shut him down.”