Make fun of someone or something means to laugh at them and make others laugh at them. Have fun means enjoy oneself.

"Make a fun" is not an expression. However, "make fun of" means that you are teasing, mocking or just joking about somebody else. For example, "Don't make fun of my hair!" or, "They were making fun of his ugly shirt". Another way of saying "make fun of" is to say, "Poke fun at". For example, "Don't poke fun at my hair". "Have fun" means to enjoy oneself.

There is no such expression as "make a fun".