  We study the existence of positive solutions for nonlocal systems in gradient
form and set in the whole $\mathbb R^N$. A quasilinear fractional Schr\"odinger
equation, where the leading operator is the $\frac Ns$-fractional Laplacian, is
coupled with a higher-order and possibly fractional Poisson equation. For both
operators the dimension $N\geq 2$ corresponds to the limiting case of the
Sobolev embedding, hence we consider nonlinearities with exponential growth.
Since standard variational tools cannot be applied due to the sign changing
logarithmic Riesz kernel of the Poisson equation, we employ a variational
approximating procedure for an auxiliary Choquard equation, where the Riesz
kernel is uniformly approximated by polynomial kernels. Qualitative properties
of solutions such as symmetry, regularity and decay are also established. Our
results extend and complete the analysis carried out in the planar case in [D.
Cassani, Z. Liu, G. Romani. arxiv:2305.15274].
