Yes, that “OTG” USB-C port on the RG350 is good for something. Here’s a quick video demonstrating gameplay using a variety of external gamepads, which supports two-player mode for PS1, Genesis, and arcade games, plus single-player GBA games.

Read my full guide here, which includes copies of the emulators that support external gamepads:
Retro handheld buyer’s guide:

00:00 introduction
00:37 PlayStation 1
01:08 Game Boy Advance
01:24 Picodrive (Genesis, Sega CD, 32x)
01:35 XMAME
01:51 compatible controllers
02:58 summary

Intro theme song sampled from “Hexadecimal Genome” by Bit Shifter: