  In this paper, we study a semilinear SPDE with a linear Young drift
$du_{t}=Lu_{t}dt+f\left(t,
u_{t}\right)dt+\left(G_{t}u_{t}+g_{t}\right)d\eta_{t}+h\left(t,
u_{t}\right)dW_{t}$, where $L$ is the generator of an analytical semigroup,
$\eta$ is an $\alpha$-H\"older continuous path with $\alpha \in \left(1/2,
1\right)$ and $W$ is a Brownian motion. After establishing through two
different approaches the Young convolution integrals for stochastic integrands,
we introduce the corresponding definition of mild solutions and continuous mild
solutions, and give via a fixed-point argument the existence and uniqueness of
the (continuous) mild solution under suitable conditions.
