Turkey would be a rather valuable ally to Germany as Turkey was where they got shipments of Chromite Ore, a vital component in Stainless Steel production so they would likely be willing to send military aid just to make sure that those shipments don't stop. Speer had a comment to the attune of "Without those shipments, production would halt within six months".
Turkey had a peace time army of 174,000 men which didn't start seeing increase until the start of 1940, at that time they mustered ~230,000 men, one armoured brigade, and three cavalry brigades with four corps stationed in the eastern "frontiers" of the nation, one corps in Thrace and one in reserve. But almost all of the equipment was pre-WW1 with rifles like the Lee Enfield, Lebel, Masuiers etc. being used, this could easily be remedied with Italian or German made weaponry but it is still something to consider. They had fortifications along the Dardanelles and along the outer regions of the country to the East, including heavy works at Erzurum, Kars, Adana amoung some others. The airforce was 370 planes of all type with only about half of them being modern even though they had over 8,000 men in their airforce. The Turkish navy consisted of the outdated battle cruiser Yavuz (ex-Goeben), 4 destroyers, 5-6 submarines, 2 light cruisers, 3 mine-sweepers, 2 gunboats, 3 motor torpedo boats, 4 minelayers and a surveying vessel.
Depending on how the events play out ITTL (I.E if Barbarossa happens the same time and way and if Turkey isn't fully occupied) this could have some huge changes. IOTL, the Soviet Black seas fleet was a pretty major player during early operations/sieges. It could also allow the Black sea to be under "axis control", with Italian and German ships being able to come in into the black sea unlike IOTL (Turkey refused to let the ships enter and the German ships that had entered had mainly been transported over-land) as well as the Romanians (The Romanian navy consisted of four destroyers, twelve torpedo boats, four gunboats, six minelayers, three amphibious landing self-propelled barges, four submarine chasers, three submarines and five midget submarines.) to defeat Filipp Oktyabrsky and prevent the vital aid the fleet gave to important sieges like Odessa in 1941 (evacuating 86,000 soldiers and over 150,000 civilians), Sevastopol that could make the city fall at the end of 1941 instead of mid 1942. This would also prevent the counter-attack at Kerch and (possibly) allow the Germans to cross over the straight themselves or be able to have the 11th army properly act as the flanking guard for AGS at the start of 1942 like they were instructed too and allow an additional 600 aircraft (including a heavy mix of Medium bombers, and dive bombers) to be deployed elsewhere.