Wayde Drew, 12, plays for Saxton FC in Richmond Hill, set up three years ago for youngsters in the inner-city community.
He was born without one lower arm and his mum Kirsty Norman said he "always tries his best at everything", but his confidence has taken a knock since starting secondary school.
The family, of Burmantofts, have launched a GoFundMe page with the Open Bionics Foundation, hoping to raise £7,000.
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If they meet the target, the charity will match the donation to raise the money needed for the new arm and hand.
“It’ll be absolutely amazing," Kirsty told the Yorkshire Evening Post.
"He’s never been bothered by it but since he started high school he hides it now, he tries to put his sleeve over it or put his arm in his pocket.
"In primary school everyone knew him, he wasn’t any different. But going to high school it’s a new lot of kids and they see Wayde as different, he’s constantly getting asked questions.
“The bionic arm will make a massive difference to his confidence. It’s simple things, like not being able to tie his own shoelaces when he’s just turned 12.”
Wayde joined Saxton FC two years ago and was immediately welcomed into the club, founded by father-of-two Jonny Nixon.
Leeds United Foundation provides a professional coach to train youngsters every week and the club is supported by the Premier League Kicks Programme.
“He feels normal there," Kirsty, 32, added.
"The first day he went down, we were both a bit panicked - he plays in goal so that makes it even harder. He’s a goalkeeper with one arm.
"But all the kids treat him like he’s the same as everybody else, they let him get on with it. He feels like he belongs."
When Jonny heard about the campaign for Wayde's bionic arm, he jumped in to support the youngster.
The club will host a fun day on its pitches and have been promoting the fundraiser on social media.
Jonny said: "He fitted in straight away and he’s never made a thing of it, and none of the other kids have.
"He’s brilliant, a real happy-go-lucky kid and a fantastic goalkeeper.
"From the time that I’ve known him he’s never let it hold him back, but as he’s getting older it’s going to benefit him so much having the working hand."
Jonny praised Leeds United Foundation which has got behind the fundraiser.
Some of the foundation's coaches will join Wayde's family as they embark on the challenging Leeds to Liverpool bike ride in April.
“Jonny has been brilliant," Kirsty added.
"If it wasn’t for him encouraging us and convincing us we could do it, I think we would’ve given up by now. We’re not well-known and it got to the point where it was overwhelming, we were struggling.
"It's good to know that somebody does want to help us and we have got the support.
“Once we’ve raised the money for Wayde, we’re going to do an annual fundraiser for somebody else who is struggling. There are so many kids that are in the same position or worse off than Wayde."
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