Definition of have on phrasal verb from the Oxford Advanced American Dictionary

 

have on

 phrasal verb
phrasal verb
 
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Phrasal Verbs

    have (got) something on

    (not used in the progressive tenses)
     
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  1. 1to be wearing something She had a red jacket on. He had nothing (= no clothes) on.
  2. 2 to leave a piece of equipment working She has her TV on all day.

have (got) something on somebody

[no passive](informal)
 
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(not used in the progressive tenses) to know something bad about someone, especially something that connects them with a crime I'm not worried—they have nothing on me.
See the Oxford Advanced Learner's Dictionary entry: have on