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The quadratic unitary Cayley graph, denoted $G_n$, is the graph with vertex set ${\\mathbb{Z}}_n$ such that two distinct vertices $a$ and $b$ are adjacent if $a-b=u^2$ or $a-b=-u^2$ for some $u$ with $1 \\leq u \\leq n-1$ and $\\gcd(u,n) = 1$. In this paper, we classify all $X_n$ admitting pretty good fractional. We also classify all $X_n$ that admit fractional revival. 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