Sure I can do that :) Thanks for asking! Any question is appreciated.

There are several classes of leptoquarks (something that I didn't mention in this post). The S₃ one consists in one of them. The '3' means that they come as triplets of particles (with different electric charges given as the superscript) and dictate how the interact through the weak interactions.

Now let's go back to your question and the y-axis. The '3' as a subscript simply connect it to the interaction of the S₃ leptoquark. The indices indicate which quark of the Standard Model and which lepton the S₃ leptoquark interacts with. Does it clarify?

In the natural system of units for particle physics (hbar = c = 1), the y interaction strength is dimensionless.