How to Say "madrileño" in Spanish
The Spanish word for “madrileño” is “gato” — C1 level.
English → SpanishC1
nounC1slang
A native or resident of Madrid (colloquial, historically specific)

Examples
Mi abuelo siempre dice que su vecino es un gato de pura cepa.
My grandfather always says his neighbor is a true-born 'gato' (a true Madrileño).
Ellos se consideran gatos porque sus familias han vivido aquí por generaciones.
They consider themselves 'gatos' because their families have lived here for generations.
Historical Context
This usage dates back to the 11th century when the inhabitants of Madrid supposedly scaled city walls 'like cats' during a battle, giving them this nickname.
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