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The function defined by $f_u(x)=ux^{d_{1}}+x^{d_{2}}$ is called the generalized Ness-Helleseth function over $\\mathbb{F}_{p^n}$, where $u\\in\\mathbb{F}_{p^n}$. It was initially studied by Ness and Helleseth in the ternary case. In this paper, for $p^n \\equiv 3 \\pmod 4$ and $p^n \\ge7$, we provide the necessary and sufficient condition for $f_u(x)$ to be an APN function. 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