Henry Winkler approached his “Barry” role as Gene Cousineau a bit differently for Season 3 of the HBO dramedy, returning Sunday on HBO after a three-year hiatus.

“Bill and Alec have two major premises,” Winkler, 76, told The Post about series co-creators/writers Bill Hader and Alec Berg (Hader stars as hitman/fledgling actor Barry Berkman). “One is no a–holes allowed and they literally hand-pick everybody. … and the crew and the actors form this delightful bond on the set.

“Their other mantra is [that] they do not want to repeat themselves. So, in the second season, I read the scripts and went to Bill and Alec and said, ‘Can I have a meeting with you? I really love this gift you’ve given me, but I don’t recognize the man you’ve written in Season 2. It was Gene in Season 1 but this guy, his name could be Bob — I don’t know who he is!’” he said of the pedantic LA acting coach, which earned Winkler his first Emmy Award in 2018.

“They said, ‘We hear you, we’re going in this direction, we will accommodate some of the things you said to us’ and Season 2 was great. For Season 3, I didn’t even bother to have the meeting. Bill and Alec are incredible leaders; they’re gentle and the know what they want, and in their structure comes freedom.

“So I just showed up, brought a Bundt cake from home, gave it to the crew and went to work.”

Season 2 ended with Gene’s startling realization that his girlfriend, LAPD Det. Janice Moss (Paula Newsome), was killed by Barry when she zeroed in on him as the man responsible for the murder that opened the series. “The scene in bed when I sit up and go, ‘My God!’ and I realized Barry Berkman did this was shot on Stage 19 on Paramount where, for nine years, we shot ‘Happy Days,’” Winkler said. “I thought there was something symmetric about that.”

As Season 3 opens, Gene is bent on avenging Janice’s murder, while Barry, who’s freelancing as a hitman (old habits die hard), is dealing with NoHo Hank (Anthony Carrigan) and the Chechen mafia and trying to make things right with Gene. Monroe Fuches (Stephen Root) is hiding out in the mountains of Chechyna while Sally (Sarah Goldberg) is filming her TV show — (very) loosely based on her stage show — and dealing with the intense pressure-cooker environment in uncharacteristic ways.

“What I can tell you is that the overall umbrella [of Season 3] is, ‘Can you change, no matter where you are in life?,’ ” said Winkler, who was sworn to secrecy regarding plot details. “That is the theme for every character. I don’t know whether [as Gene] I actually achieve that or not, but that’s the train that everyone got on.”

What is revealed in the first two episodes of Season 3 is the enmity that his Hollywood brethren feel toward Gene. (One casting director’s response to hiring Gene for a small part: “Life’s too short.”) “We find out that there is a litany of curse words that people have used about Gene that would make a sailor blush,” Winkler said.

Winkler said the two-and-a-half-year layoff between seasons of “Barry” (Season 3 began shooting last summer) was, in the end, beneficial to his portrayal of Gene.

“It’s like riding a bike,” he said. “When you do a play and then it goes into repertory or you don’t do it for a while or you do a revival years later, that play has lived in you and the character has lived in you. It’s gestated into a richer form. The material this year [on ‘Barry’] without joking or exaggerating … was the most intense material I have ever done in my entire career, starting with June 30, 1970, when I showed up at the John Drew Guild Theater in East Hampton for repertory.

“At the [Season 3] premiere, we were all watching the first two episodes at the HBO party and, after it was over, I looked at every one of those actors and thought to myself, ‘I am so lucky and I am so proud that I’m here and I’m with them.’ “

The Season 3 premiere of “Barry” airs Sunday, April 24 at 10 p.m. on HBO.