Clarke Schmidt is getting his most extended shot to prove he can be a major league starter. He’s just not making very much of it.

Schmidt continued to struggle on Tuesday night, again failing to make it out of the fourth inning as the Yankees lost to Shohei Ohtani and the Angels, 5-2, in The Bronx.

Through four starts this season, Schmidt has yet to throw a pitch after the fourth inning.

He lasted 3 ²/₃ innings against the Angels and gave up four runs, pushing his season totals to 14 ¹/₃ innings and 14 earned runs allowed on 22 hits, four of which were four home runs — including Ohtani’s two-run homer in the first inning Tuesday.

Still, manager Aaron Boone said after the game that the Yankees will continue to let Schmidt work things out at the major league level.

“I mean, he’s one of our starters right now,” Boone said when asked if putting Schmidt in lower-leverage situations might suit him better. “I can’t turn down the leverage at the start of the game. We’re a little banged up in the rotation right now. He’s gotta go out there and find a way and get to that next level right now. We don’t really have that luxury right now.”

The Yankees (10-7) were high on Schmidt this spring, which he began in a battle for the fifth starter spot with Domingo German.

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But because of an early injury to Carlos Rodon, it never turned into much of a competition.

Add in Luis Severino’s injury, which forced Jhony Brito into the rotation for the first month of the regular season, and the Yankees are not exactly flush with options to replace Schmidt until Severino returns.

In the meantime, Schmidt continued to show a mix of potential and frustration against the Angels (9-8), giving up two runs in the first inning and two more in the fourth inning, while retiring eight straight batters in between.

“A little bit of that inconsistency,” Boone said. “You see a lot of good in there and times where he’s not controlling the strike zone where he needs to.”

Ohtani became the third left-handed hitter to homer off Schmidt this season, crushing a 2-0 slider in the first inning.

The Yankees had a chance to strike back immediately, loading the bases with two outs in the bottom of the first, before Oswald Peraza grounded out in his first MLB at-bat of the season.

Schmidt recovered with sharp second and third innings, but ran into more trouble in the fourth.

Mike Trout led off with a double down the left-field line and came around to score when Anthony Rendon sliced a line drive to right field.

Hunter Renfroe then doubled to the left-field corner and Rendon raced around from first to make it a 4-0 game.

Schmidt retired the next two batters before hitting Zach Neto on the hand with a sinker. That was the last batter he faced.

“Obviously you want to be in a better spot, in a better groove and go deeper in games and do the small things where you’re putting your team in a chance to win every single time throughout the whole game,” Schmidt said. “There’s things I need to work on and things I need to do better. But I’m going to continue to put the work in and continue to compete and be better each time out.”

The Yankees finally scratched across a pair of runs in the bottom of the fourth on Anthony Volpe’s bases-loaded walk and Aaron Judge’s sacrifice fly.

But it was far from enough on a night when they stranded eight men on base and fell behind early, just as Schmidt did on the mound.

“Early in the counts, having count leverage is the key, especially to good hitters like they have,” Schmidt said. “When I have my count leverage, I normally have a lot of success. So being able to get more first-pitch strikes is the key overall.”