Next vs This (time)

Could someone tell me which one should I use? In the case that today is Monday (1/15), which one is correct?
a) I can meet you on next Friday (1/19).
b) I can meet you on this Friday (1/19).

Thank you

[BobK]

You wouldn't say 'on' if you use 'this'.

I can meet you on Friday[ - this Friday] (In this case you might feel you need to add 'this Friday', to make it clear);
or
I can meet you this Friday

"Next" is a week later than "this", but only a few days more than a week. On Thursday you might say 'next Friday' (meaning 'in 8 days'); but on Monday 15th, you would say I can meet you on [the] Friday [of] next week or I can meet you a week this Friday .

b

[Humble]

Hi,
I’ve also heard Friday week (=on Friday next week)

[BobK]

- I forgot that. It works with 'fortnight' (two weeks) too - 'Friday fortnight' - but not with 'month' or 'year'; for those you need to spell it out - 'a month/year next Friday'. (I don't think the word 'fortnight' is current AmE.)

b

[Casiopea]

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Today is Monday, January 15th
a) I can meet next Friday. <Meaning, I can meet on January 26th>
b) I can meet this Friday. <Meaning, I can meet on January 19th>

In other words,

I can meet next Friday, on January 26th.
I can meet this Friday, on January 19th.

All the best.

[BobK]

Re: 'fortnight'

This may not be used in America, but I think it's understood. In the '80s, when I was working for DEC, an American software engineer writing the on-line help for the VMS operating system used the word 'micro-fortnight' to mean 'second' (as a fortnight is 1209600 seconds and a binary million is 1048576). I think he was making a joke about UK software engineers being recruited to work on DEC products). Quite possibly users of OpenVMS - of whom there are still a few - can still see this.

b

[Casiopea]

The Word Detective

"Fortnight," which means a period of fourteen days, is a contraction of the Old English phrase "feowertiene niht," which meant "fourteen nights." (The ancient Germanic peoples from whom we lifted the phrase measured time in nights, not days.) A related term, "sennight," means a period of seven days (from the Old English for seven nights, "seofon niht"), but is very rarely heard today.

"Fortnight" itself is pretty rare in the U.S., although it is still in common use in Britain. The entire British way of speaking about the immediate future, by the way, often confuses American visitors. While in the U.S. we might say "I'll pay you two weeks from Tuesday," in Britain they would say "I'll pay you Tuesday fortnight," or "Tuesday week" if they were going to pay you a week sooner. The British also follow the date format "day, month, year" (as in "4 July 1999" or "4/7/99"), rather than our familiar "month, day, year" form.

[rmk]

Hi everyone!
I'm very thankful for all the answers. I've registered under this username.

[Casiopea]

You're most welcome, and welcome, rmk.