There is currently no experimental evidence that suggests quarks are "made of" anything smaller; they are considered a fundamental particle, essentially a building block of matter. However, we should specify that the emphasis is on our uncertainty rather than our certainty that this is the case; the quark might be made of something smaller, and we simply lack the technology or the procedure to properly investigate and confirm the existence of that substructure. A number of theories, such as the "preon" put forth the idea that the quark has a substructure and that this simplifies rather than complicates our explanation of empirical observations in particle physics, but to date there is little or no indication that preon/substructure explanations are superior AND supported by evidence compared to the Standard Model, which currently depicts quarks as fundamental.
A (very oversimplified) interpretation of the quark is that it is a combination of multiple "ripples" in different fields that are all superposed in the same location, making it "point-like" in that it has no surface area, but it occupies a definite volume within which its characteristics are established. This is distinctly different from having specific sub-structures occupying a volume within the volume of the quark; if anything, it's more like the quark is a series of substructures all occupying the same three-dimensional location, and inseparable from each other.
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