The Denver is the only ship in licensed sources, to date, to be identified as a Yorkshire-class vessel. The class designation itself comes from the Star Trek Encyclopedia and does not appear in TNG episode: "Ethics".
There is probably a USS Yorkshire that would be the first vessel of this series, but such a ship has not been referenced in Star Trek publications to date.
A ship description was mentioned in several supplements to the Last Unicorn Games role-playing games released following the loss of their Star Trek license, which refers to this class of starship being a type of armored transport which entered service in 2365.
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Two additional Yorkshire-class vessels are also listed in addition to the Denver: the prototype USS Yorkshire and the USS Cornwall (NCC-55938). The entry on the Cornwall indicated that she landed troops on Cardassia Prime during the assault on the Chin'toka system in 2374.