Bearing in mind subsequent changes (including the 2020 phase-out currently in the works), a 2013 press release by Northrop Grumman said:
Turkish Aerospace Industries, Inc. (TAI), a subcontractor to Northrop Grumman, delivered its first F-35 Lightning II center fuselage to Northrop Grumman and Lockheed Martin at a ceremony held at TAI's facilities in Ankara, Turkey, on Dec. 11, 2013.
Once the program reaches full rate production, TAI will support F-35 final assembly lines in the United States and Italy by shipping one center fuselage every 10 days. TAI's center fuselages will be integrated into the Turkish F-35 aircraft as well as other participating nations' aircraft.
In addition to building center fuselages as a Northrop Grumman subcontractor, TAI is the single source for center fuselage metallic assemblies for F-35A, selected composite components for all F-35 variants, and is one of two sources for composite air inlet ducts for F-35A, and air-to-ground alternate mission pylons for all F-35 variants.
Note that the F-35A variant is used by the US (and also by other countries).
And from a 2009 press release (in which the CTOL variant probably refers to the later F-35A):
The assemblies from TAI will be used in center fuselages for F-35 conventional takeoff and landing (CTOL) variants. Northrop Grumman, a principal member of the Lockheed Martin-led F-35 industry team, is currently assembling those CTOL center fuselages in Palmdale, Calif., as part of the second phase of F-35 low rate initial production.
"We are very encouraged by TAI's steady progress in maturing the production and assembly processes that will be required to eventually produce 400 center fuselages for the program," said Mark Tucker, vice president of tactical systems and F-35 program manager for Northrop Grumman's Aerospace Systems sector.
TAI is scheduled to produce this metallic structural assembly for all CTOL center fuselages currently planned for the F-35 program, added Tucker. All of the assemblies will be produced in TAI's manufacturing facility in Ankara, Turkey. Northrop Grumman previously produced the assembly in Palmdale.
Northrop Grumman is responsible for the design and production of center fuselages for all three variants of F-35 aircraft: CTOL; short take-off, vertical landing; and carrier-compatible. The F-35 Lightning II program expects to build more than 3,100 aircraft.
So while TAI was scheduled to produce only a fraction of the total center fuselages (as a second source), they were intended to be the sole source of the "center fuselage metallic assembly" for the CTOL variant (F-35A).