Let \(q=p^m\) , where p is an odd prime and m is a positive integer, and let \(\mathbb {F}_{q^2}\) denote the finite field with \(q^2\) elements. In this paper, we determine the boomerang uniformity of the power function \(f(x)=x^{q+2}\) over \(\mathbb {F}_{q^2}\) for \( q \equiv 1 \) or \( 3\) (mod 6). Furthermore, for the case \(q\equiv 3\) (mod 6), we also present additional properties of its boomerang spectrum. The paper employs refined techniques from algebraic number theory and the theory of finite fields, using tools like character sums to analyze the boomerang properties of functions over finite fields, which are believed to be applicable for addressing similar problems.
