The phrase "Patriots Day jersey" primarily functions as a noun phrase. The components combine to identify a specific category of merchandise: a jersey related to or commemorating Patriots' Day.
Analyzing the individual elements, "Patriots Day" acts as an adjectival modifier, specifying the type or occasion associated with the jersey. "Jersey" is the core noun, denoting the garment itself. Therefore, the phrase operates syntactically as a compound noun, where the adjectival part classifies the jersey further.
In conclusion, the essential part of speech for this phrase is noun. The subsequent adjectival description provides extra descriptive information that narrows down what kind of jersey is being referenced or sought after.