  In this paper, we consider the extended stochastic Navier-Stokes equations
with Caputo derivative driven by fractional Brownian motion. We firstly derive
the pathwise spatial and temporal regularity of the generalized
Ornstein-Uhlenbeck process. Then we discuss the existence, uniqueness, and
H\"{o}lder regularity of mild solutions to the given problem under certain
sufficient conditions, which depend on the fractional order $\alpha$ and Hurst
parameter $H$. The results obtained in this study improve some results in
existing literature.
