Can tinea versicolor be controlled by having a particular diet like no yeast or sugar?

No. Tinea versicolor is a chronic fungal skin infection. To make it go away (temporarily), you have to kill the fungus by using anti-fungal medications like clotrimazole, ketoconazole, or miconazole. Otc dandruff shampoos applied for 10 minutes each day in the shower may also help. It is not caused by eating yeast or sugar. It often recurs, especially in warm months/climate.
Try shampoo. While some believe that diet can effect t. Versicolor, the practical nature of doing it is a bit extreme. Have you tried rubbing selsum blue shampoo into the skin and letting it sit on tje skin for 15 min. Prior to showering?