Blackfishing is a term which describes a white person taking on black cultural references for their own gain.
Speaking during an Instagram live, Jesy commented: "My intentions were never ever to offend anyone and it actually does really hurt me that I may have offended people and like hurt people's feelings by genuinely celebrating something that I love."
Nicki said: "There ain't nothing new with white people wearing wigs."
Jesy implied her tan was the result of a trip to Antigua shortly before filming her debut solo clip.
Nicki also called Jesy's former band member Leigh-Anne Pinnock a "clown" for allegedly messaging a TikToker over the weekend about Jesy's "blackfishing".
"You don't have to come out and try to ruin anyone," Nicki said. "Let her [Jesy] have her time. If you was in this woman's group and you ain't talk about this sh*t for 10 years and as soon as you see she's got a video coming out with Nicki Minaj and Puffy now you're sending the stations text messages and all this sh*t."
Jesy did not speak during Nicki's outburst against Leigh-Anne laughed as Nicki trolled Leigh-Anne and told the new mum-of-two to "shove the messages up her motherf*****g a**".
It comes after Nicki was also spotted leaping to Jesy's defence in a TikTok comment which she later deleted, writing that she wasn't the only celeb to appear on camera with a tan and big lips.
"So all these reality stars y'all worship with big lips and tans r ok but Jesy's where y'all draw the line huh??",she said.
She subsequently promised to "get into some thangz" during the live - and that she did.
It wasn't just Jesy's skin-tone that got tongues wagging in the Boyz video, it was also the song's lyrics, and her accent, which some claimed was put on.
"I like the tattoos and them gold teeth / Tough to make me feel like I'm a baddie," she sung at one point, while also claiming to like her men "hood" and "so damn taboo".
Speaking on blackfishing allegations put to her in the past, Jesy told Vulture: “The whole time I was in Little Mix I never got any of that.
"And then I came out of [the band] and people all of a sudden were saying it. I wasn’t on social media around that time, so I let my team [deal with it], because that was when I’d just left.
“But I mean, like, I love Black culture. I love Black music. That’s all I know; it’s what I grew up on. I’m very aware that I’m a white British woman; I’ve never said that I wasn’t."
She later added that she would "never intentionally do anything to make myself look racially ambiguous, so that’s why I was initially shocked that the term was directed at me".
Jesy's new single comes after her departure from Little Mix last December. She signed a record deal with Polydor in May.