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We obtain the Wang-type integral inequalities for compact minimal hypersurfaces in the unit sphere <inline-formula> <math display="inline"> <semantics> <msup> <mi>S</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </semantics> </math> </inline-formula> with Sasakian structure and use these inequalities to find two characterizations of minimal Clifford hypersurfaces in the unit sphere <inline-formula> <math display="inline"> <semantics> <msup> <mi>S</mi> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </semantics> </math> </inline-formula>.