Turkey's recent operations in Syria against Kurdish groups – some of which the United States supports – raises question: If the shooting started, who would win a war between Turkey and the United States? It's not implausible, especially after the failed coup against Recip Tayyip Erdogan.
In some respects, Turkey would represent a significant challenge to the United States military. In terms of airpower, FlightGlobal.com notes that the Turkish Air Force is very modern, with over 250 F-16s on inventory. The same goes for the Turkish Navy. The Navy has some capable surface combatants. The roster includes eight modernized Oliver Hazard Perry-class frigates, eight German MEKO 200 frigates, and an indigenous corvette class.
The war could easily start with Turkish forces that are targeting the Kurds accidentally killing some American troops. Since the United States and Erdogan don't have the best of relationships (a prominent critic of Erdogan has taken refuge in the U.S.), things could escalate from there as the Turks would try to intern American Air Force units at Incirlik Air Base.
Nice Try, but Turkey Doesn't Have What it Takes
While getting the planes would be an iffy proposition (they would probably get airborne and make for Greece, Israel, or other friendly countries), the Turks would likely be able to capture American ground crews. The United States would be demanding their release, and should Erdogan not comply, the war would start.
Despite a lot of modern systems in the Turkish armed forces, Turkey's military would likely lose. The United States would leverage F-22 and B-2 bombers to hit Turkey. Similarly, Greece, which has had some long-standing disputes with Turkey, might also join in. Turkey would likely inflict some serious casualties on the U.S., though, and it would have the leverage of the POWs. An American victory, though, would also have the effect of shattering NATO. In essence, there is no winner that would emerge in a Turkish-American War.