In this paper, we investigate the nonlinear Chern-Simons-Schrödinger equation \(\begin{aligned} -\Delta u+\left( \frac{h_u^2(|x|)}{|x|^2}+\int ^{\infty }_{|x|}\frac{h_u(s)}{s}u^2(s)\textrm{d}s\right) u= -a|u|^{p-2}u+(I_{\alpha }*F(u))f(u)\ ~~\hbox {in}~\mathbb {R}^{2}, \end{aligned}\) where \(a>0\) , \(p\in (2,3)\) , \(\alpha \in (0, 2)\) and \(\begin{aligned} h_u(s)=\int ^s_0\frac{\tau }{2}u^2(\tau )\textrm{d}\tau =\frac{1}{4\pi }\int _{B_s}u^2(x)\textrm{d}x \end{aligned}\) is the Chern-Simons term, \(I_{\alpha }: \mathbb {R}^2\rightarrow \mathbb {R}\) is the Riesz potential, \(f: \mathbb {R}\rightarrow \mathbb {R}\) admits critical exponential growth in the sense of Trudinger-Moser inequality. Under certain assumptions on f, we develop a direct energy estimation method to overcome the challenges posed by the critical Choquard type exponential term. Additionally, we establish the existence of a mountain-pass type solution for the equation using Jeanjean’s monotonicity trick in combination with some innovative analytical techniques.
