In this paper, we consider the singular set for suitable weak solution of the 3D incompressible hypodissipative Navier-Stokes equations, when the dissipation is given as a fractional Laplacian \((-\Delta )^s\) for \(s\in (\frac{3}{4},1)\) . First, we prove that the Minkowski dimension is bounded by \(\frac{(3+2s)(135+927s-1668s^2+912s^3-192s^4)}{9(16s^3-40s^2+57s+9)}\) , which refine the result from (Kwon-Ożański 2022 J. Funct. Anal. 282 109370). Meanwhile, we generalize the result in (Koh-Yang 2016 J. Differ. Equ. 216 3137-3148) which was restricted to the \(s=1\) . Moreover, for a given open subset \(\omega \subset \mathbb {R}^3\) and a given moment of time \(t\in (0,\infty )\) , we obtain an upper bound for the number of points of the singular set \(\sum (t)\cap \omega \) , where \(\sum (t)=\{(x,t)\in \sum \}\) and \(\sum \) is the set of singular points for suitable weak solution of fractional Navier-Stokes equations.
