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During the two US Barbary Wars, Tripoli and the Barbary States were nominally part of the Ottoman Empire.
With a POD after 1790 have either of the Barbary Wars end up in wars between the United States and the Ottoman Empire. Preferably this should not be part of a Pan European War started by other factors. (so US/UK/Coalition vs. Napoleonic France and the Ottomans started by Napoleonic efforts to keep Louisiana isn't what I'm looking for)
For bonus points have the 2011 military intervention in Libya (called by some the 3rd Barbary War) lead to Turkish intervention on the Qadaffi's side.