  We consider a non-local Shr\"odinger problem driven by the fractional Orlicz
g-Laplace operator as follows \begin{equation}\label{PP}
(-\triangle_{g})^{\alpha}u+g(u)=K(x)f(x,u),\ \ \text{in}\
\mathbb{R}^{d},\tag{P} \end{equation} where $d\geq 3,\
(-\triangle_{g})^{\alpha}$ is the fractional Orlicz g-Laplace operator,
$f:\mathbb{R}^d\times\mathbb{R}\rightarrow \mathbb{R}$ is a measurable function
and $K$ is a positive continuous function. Employing the Nehari manifold method
and without assuming the well-known Ambrosetti-Rabinowitz and differentiability
conditions on the non-linear term $f$, we prove that the problem \eqref{PP} has
a ground state of fixed sign and a nodal (or sign-changing) solutions.
