In German something from Baden is Badisch, and somebody from Baden is a Badenser or a Badener (there have been long and heated debates over which is right so I won't take sides)
In French Baden is calkled Bade and the adjective is Badois.
In English the historical state of Baden which existed until the 1870s or thereabouts is called the Grand Duchy of Baden (Grossherzogtum Baden). Today Baden does not exist as a political entity but is part of the federal state of Baden Württemberg which goes by the same name in English.
The region within that state that is called Baden is also called Baden in English.
I don't think there is a commonly used adjective that describes something from Baden. I think a wine from Baden would be a Baden wine rather than a Badener wine or something like that.