請問 I wish you a great time on Friday.?

別聽他們胡說.

I wish you a great time on Friday. 是對的.
改成 I wish you have a great time on Friday? 就錯了喔!

請相信prisoner26535, 信者得救！

I wish you a great time on Friday. ( O 啦！)

[1] I wish you a great time on Friday. ( ✔ ✔ )
--- a short form for : "I wish that you would have a great time on Friday."

[2] I wish you have a great time on Friday. (x - ∵ grammatically incorrect)
應改為:-
I wish that you will/would have a great time on Friday. ( ✔ )
I wish that you can have a great time on Friday. ( ✔ )

I wish you a great time on Friday.
句意應該該是預祝對方在未來(將來)的星期五的某節目愉快吧。
其實句子未盡完成;
由於是預祝將來的，可以用很formal的未來時態加在you後作為給對方的"動詞"：
I wish you will have a great time on Friday.
或簡化口語化一點用infinitive to給對方指示式的句法：
I wish you to have a great time on Friday.

wrong!

You need a verb after you