<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-folds, string junctions, and 4D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> SCFTs

$S$-folds are a nonperturbative generalization of orientifold 3-planes which figure prominently in the construction of four-dimensional (4D) $\mathcal{N}=3$ superconformal field theories (SCFTs) and have also recently been used to realize examples of 4D $\mathcal{N}=2$ SCFTs. In this paper, we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an $S$-fold. We develop an $S$-fold generalization of orientifold projection which applies to nonperturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the $S$-fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D $\mathcal{N}=2$ SCFTs. Furthermore, this provides a prescription for how to define F-theory in the presence of $S$-folds with discrete torsion.