Meet Patricia Dombrowski, the rapping heroine of “Patti Cake$.” A North New Jersey girl with a gift for rhymes and off-the-cuff insults, Patti tends bar at the local dive while dreaming of making it big in the music industry. She has just two problems: She’s not only Caucasian but noticeably overweight. “A white Precious” is how one neighborhood naysayer dismisses her.

In some ways, Patti recalls Paul Potts, the real-life opera tenor played by James Corden in “One Chance,” or even the animated elephant who yearns to belt out pop tunes in last year’s “Sing!” What differentiates this particular underdog story is the gritty backdrop of North Jersey, where writer-director Geremy Jasper was raised. Patti lives in an unnamed town where she scrambles for part-time work, forks the money over to her hung-over mother, Barb (Bridget Everett), and cares for her ailing Nana (a wonderfully cranky Cathy Moriarty). This is a neighborhood so rough — at one point, Patti’s smart mouth gets her a fat lip — that anyone who can’t take it is told to “go back to Newark.”

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There’s a whimsical vibe to this movie as well. Patti, played by an excellent Danielle Macdonald (an Australian actress, though you’d never know it), has teamed up with another unlikely wannabe: Jheri, an affable Indian dude who works at a pharmacy but aspires to be an R&B crooner (he’s played by Siddharth Dhananjay, whose spoof music videos on YouTube landed him the role). But these two are Frankie and Annette compared to an outcast named Basterd (Mamoudou Athie) who hammers out industrial goth-rock in a filthy squat near the highway. Together, they form the hip-hop trio PB&J and begin shopping around their demo CD. (Look for MC Lyte, a female rap pioneer, as DJ French Tips.)

A hit at this year’s Sundance festival, “Patti Cake$” is an extremely rough-edged movie with some uncertain performances and a script that occasionally loses its way. Still, the raw spots only prove that “Patti Cake$” is the real deal — an original, handmade piece of work from a filmmaker bursting with creativity. (Jasper also wrote all the original songs, and co-wrote the score with Jason Binnick.) It’s impossible not to root for Patti, and for this scrappy, irrepressible movie.