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Let $A,ϵ>0$ be arbitrary. Suppose that $x$ is a sufficiently large positive number. We prove that the number of integers $n\in (x,x+x^{\theta }]$, satisfying some natural congruence conditions, which cannot be written as the sum of three squares of primes is $\ll x^{\theta }{(\log x)}^{-A}$, provided that $\frac{7}{16}+ϵ\le \theta \le 1$.