If you want only the ring pattern to be tinted, it should be possible by having only the ring in white color, with the rest of the image being black. This way, when we apply a tint, the tint color is multiplied with the white color (1,1,1) and thus gives a tinted ring pattern, while the black region when multiplied (0,0,0) ends up remaining the same.
Also make sure that you have set the Compression Settings & Texture Group for your texture to UI.
