From my travel guide I get the information that this castle was founded by the Knights of St. John of Jerusalem, who were based on Rhodos but liked the opportunity of having a stronghold in Bodrum when that was captured in 1402. It’s called the Castle of St. Peter and houses the excellent (that’s me writing) Museum of Underwater Archeology.
The have some old ship wreck and lots of glassware and other stuff salvaged from the sea. Also an interisting exhibition of the amphora through the ages.