Batman has had plenty of movies and TV shows with his name. The Joker can even boast a couple of solo films. Now it’s time for the spotlight to shine on a Gotham City menace who knows fowl play.

“If you asked Oz if he's happy to have his own show, he'd be like, ‘It's about damn time,’ ” says “The Penguin” creator/writer Lauren LeFranc about her title gangster in the new HBO crime drama.

Transformed by makeup and prosthetics, Colin Farrell introduced a new version of the Penguin in director Matt Reeves’ “The Batman” two years ago. Instead of focusing on Robert Pattinson's Dark Knight detective, the eight-episode “Penguin” spinoff series (premiering at 9 p.m. EDT/PDT Sept. 19 on HBO and Max, weekly Sundays starting Sept. 29) follows Farrell's mobster Oz Cobb making big moves to run Gotham City’s underworld. (Pattinson and Farrell will tussle again in "The Batman: Part II," which films next year.)

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Set a week after “The Batman,” the new show finds crime-ridden Gotham devastated by flooding and there’s a scramble to fill the power vacuum following the death of mob boss Carmine Falcone. A lower-level henchman with the Falcones, the ambitious Oz eyes a way to own the town’s drug trade and play the Falcone and Maroni families against one another with the help of his young right-hand man, Victor Aguilar (Rhenzy Feliz). But the return of convicted serial killer Sofia Falcone (Cristin Milioti) after a 10-year stint in Arkham Asylum threatens that rise to power.

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Farrell says Oz was meant to just be a “red herring” in the first “Batman” film – “He was behavioral, he was kind of cock-of-the-walk” – but the series digs into “the psychology of him as a man, and how far he's willing to go. And also through flashback, get into some really painful details about his upbringing that don't justify but somehow describe why he is a version of the man that he is.”

‘The Penguin’ mines a Batman baddie’s childhood for origin story

Oz is far from the fine feathered finks played by Burgess Meredith and Danny DeVito. Working in Reeves’ more realistic version of Gotham, LeFranc wanted this Penguin's origin story to be rooted in family and for him to be an underdog – which is why his name is Oz Cobb in the show and not the more familiar Oswald Cobblepot. In DC Comics canon, that's a wealthy Gotham family and “his name means something,” LeFranc says. She didn't want Oz to have that, as he'd be "so desperate to achieve something if he started from a place of being without something.”

Farrell adds Oz’s drive was “born of pain experienced in his formative years as a child. His ambition is calcified through the years and throughout the telling of this tale over eight hours, it becomes darker and more sinister and more relentless in his pursuit of his dream of having ultimate power and ultimately making his mother proud.”

When not doing crimes, Oz takes care of his beloved mom (Deirdre O’Connell), and LeFranc thought she should inform who he is as well. “I wanted him and his mom to have a very twisted, unusual, slightly Oedipal relationship,” LeFranc says. Plus, “he would respect someone like Sofia Falcone more than other people because he has a mother who has so much gravitas and shown him how powerful women can be.”

Cristin Milioti embraces her 'pretty great' villain era

Of all the characters in “The Penguin,” Sofia is the most like a classic Batman villain, having done time in the iconic Arkham prison after being nicknamed “The Hangman” and come out a deranged version of her former self. “She's sleeping in her closet, clawing at her neck every night,” Milioti says. Her father Carmine (played in the show by Mark Strong) told Sofia she was the rightful heir to the crime family until she goes through something “unfathomable,” the actress adds. But instead of escaping a bad situation, “it made sense to me that she would return and be like, ‘OK, I'm going to get that power and I'm going to keep going.’ ”

Oz looks like a ghost when he sees that Sofia’s back: There’s a deep history between them, and a betrayal as well, that creates serious friction. “They're such excellent adversaries for each other, but they also are kindred,” Milioti says. “She completely sees through all of his B.S., obviously. Especially in the first couple episodes, you think, ‘Actually if they were able to work together, they could probably do some pretty great and sinister things.’ But then it's so much more delightful that they become adversaries. The ways in which they battle it out are so deep and psychological and hurtful. And you can only do that with someone that you know really well."

Colin Farrell’s Penguin finds a young orphan to help his cause

With a scarred face and waddle (thanks to a bad foot), Oz looks the Penguin part but also has a charm and raconteur air about him. “Oz says and does whatever he wants,” LeFranc says. “It's fun to write someone who's off kilter and a jerk and a little mean and a little funny and breaks the rules.” And when he gets into trouble, Oz leans on Victor, an orphaned teen the gangster takes under his wing.

“He sees that Victor has a stutter and has been bullied as a kid because of what differentiates him from everyone else, his physical impediment,” Farrell says of Oz, who stands up for Victor when others don’t treat the kid with respect. “He wants Vic to be the strongest version of himself.

“But one person's care is another person's cruelty. Oz caring for you does not mean that you're ever fully safe in his company. He will literally do whatever it takes to get ahead in life.”