“A mother’s love” comes in a most unusual package in “A Thousand and One,” an intimate mother-and-son character study that’s most rewarding in sharing the details of barely scraping by in New York City.

A.V. Rockwell’s debut feature is built on a bracing, abrasive performance by singer-turned-actress Teyana Taylor. Her character, Inez, only lets us see “warmth” in tiny doses. It’s as if she’s learning that along the way, because as a child of “the system,” growing up in state care, she has no clue how to show it.

“A Thousand and One” is the sort of movie that lets the viewer judge Inez, who spirits a little boy she’s come to know and pity out of a hospital and out of that foster parent/group home/social worker machine she experienced growing, and raise him as her own. We judge her, first scene to last. But Taylor’s defiant performance demands that by the closing credits, we consider her in her totality — the crime, and its motives, methods and above all else, results — and wonder if we’ve been right or wrong about her all along.

We meet her on Riker’s Island in the New York at the beginning of Rudolph Guiliani’s administration. She’s doing a fellow inmate’s hair, set to be released back into a city that was — in 1994 — about to be transformed, for good and bad, by shifting attitudes, fading compassion and a new winner-take-all economic reality.

Whatever Inez went to jail for, her former hair salon boss doesn’t want to hear about it. He shoves money in her hands just to get rid of her. She’s scrambling to get herself employed or self-employed, just to find a place to live that isn’t in the open air.

And then she spies a silent child of about five (Aaron Kingsley Adetola) mixed in the with the children in a group home in her corner of Brooklyn. She starts talking to him, relating to him what she went through “when I was in foster care.” She buys him ice pops, and always calls out to him when he and the bigger kids in the home come out to play.

Inez sees Terry, and calls him “T.” She watches him ignored or bullied by the other kids and the adults in charge. When he gets hurt, she hears about it and makes her way to the hospital where he was taken. He comes to regard her, at her suggestion, as his mother. When he asks her, “Why do you keep leaving me?” she takes action.

They slip away, make their way from Brooklyn to Harlem, where she still has one friend (Terri Abney) who’ll take her, and this child — who has made the newspapers — in. Living briefly with Kim and her disapproving mother (Delissa Reynolds) we see patterns emerge, poor and working class Black women taking a keen interest in a child and how he will be raised, and Inez’s fitness for ensuring that upbringing.

She is unfiltered, hot-tempered and impulsive, with “a rap sheet as long as the sidewalk,” one former employer notes. But she’s got this kid now, and she’s capable of forming a plan.

She’ll get a place to live, get work and perhaps wait for her man, Lucky, to get out of jail, feeding and caring for T the best she knews how, all while laying low to keep him and herself from being caught.

Terry will be left at home along in dumpy apartments. When she’s questioned about why he isn’t in school, she’ll finesse that. And when Lucky (William Catlett) gets out, maybe they’ll form “a family.”

There’s a nobility in this story that keeps popping out at the most unexpected moments. Lucky may say “He ain’t my kid,” and be reluctant to engage with the shy, untrusting child. But he does. He and Inez fight, break up and make-up, even after they get married. But troubled as all that may sound, Terry has people looking out for him, getting him fed, housed, clothed and to school.

He’s in on the conspiracy, which he seems to forget as he ages into his teens (Aven Courtney plays him then) and approaching graduation (Josiah Cross is 17 year-old Terry). Wherever Mom got that birth certificate, Terry thrives in school.

The three young actors who bring Terry to life show us a boy who never quite grows out of his shyness, never makes much of his facility at schoolwork and rising prospects. But we notice.

Taylor’s uncompromising, arms-lenth Inez, a mother of uncertain means and dubious methods, is never entirely likeable. But as we watch her we do the math she did way back in the day, in that hospital. She’s keeping her promise, making his life upbringing better than hers was.

She’s a net positive in his life, any way you add it up.

As as writer-director Rockwell makes clear in obvious and more subtle ways, that’s no mean feat in a New York increasingly hostile to the working poor and others at the bottom of the economic ladder. Every change in “stop and frisk” (“hassle Blacks and Latinos”) policing, in housing regulations (Yuppy slumlord gentrification), in taxation to cover all manner of “public” services — from schools and transit to social services — hits Inez, Lucky and Terry and people like them the hardest.

Rockwell’s achievement is to script a simple character study, cast it with an actress up to turning it into a tour de force, and making the entire enterprise a history lesson in the true cost of Giuliani’s “more livable city” experiment.

Rockwell may never again take us completely by surprise, and really, you only get to be the darling of the Sundance Film Festival once. But he’s conjured up a debut feature that’s involving, informative and even moving, despite its unlikely heroine’s best efforts to prevent that.

Rating: R, sexual situations, smoking, profanity

Cast: Teyana Taylor, Aaron Kingsley Adetola, Aven Courtney, Josiah Cross,and William Catlett

Credits: Scripted and directed by A.V. Rockwell. A Focus Features release.

Running time: 1:57