Fetching details from the dictionary...
supervision; management
みかじめを要求ようきゅうされて困っこまった。
I was troubled by being demanded protection money.
みかじめの支払いしはらいを拒否きょひした。
I refused to pay the protection money.
みかじめを取るとる行為こういは違法いほうだ。
The act of taking protection money is illegal.