The next Friday or Next Friday is practically nonmeaningful. I mean what's next doing there? If Friday comes, it'll be just Friday, why next? To be precise, you should call it this Friday which'll mean that you are talking about the Friday which is coming. Something like this week, this month or this year which means following whatsoever period.

Let's consider this case - Today is June 9 (Monday). So, I'll refer June 13 as This Friday. You'll find this good use of phrase on TV channels. They always advertise or notify the viewers that way (Say...The Matrix THIS FRIDAY on AXN) However, if you want to refer to Friday falling on June 20, then putting next in the same sentence makes sense. I'd call it this way:

My exam is on this Friday (13th) and Paul's on next Friday (20th).

BUT whatever it is, to stay clear, always mention the date to avoid ambiguity especially if you are talking on a serious deal. :)

The next Friday or Next Friday is practically nonmeaningful. I mean what's next doing there? If Friday comes, it'll be just Friday, why next? To be precise, you should call it this Friday which'll mean that you are talking about the Friday which is coming. Something like this week, this month or this year which means following whatsoever period.

Let's consider this case - Today is June 9 (Monday). So, I'll refer June 13 as This Friday. You'll find this good use of phrase on TV channels. They always advertise or notify the viewers that way (Say...The Matrix THIS FRIDAY on AXN) However, if you want to refer to Friday falling on June 20, then putting next in the same sentence makes sense. I'd call it this way:

My exam is on this Friday (13th) and Paul's on next Friday (20th) or as SydneyAustraliaESLTeacher (too big ;)) says - Friday next week or the following Friday (the Friday that follows this week's Friday in this case).

BUT whatever it is, to stay clear, always mention the date to avoid ambiguity especially if you are talking on a serious deal. :)