Please explain me. What is correct way?
Have you got any reply? OR
Have you gotten any reply?

In American English:

Have you got any reply? = Do you have any reply?
(This is present tense. This uses ‘have got’ idiomatically with a meaning similar to ‘possess’, and you could simply use the verb ‘have’ without the word ‘got’ instead.)

Have you gotten any reply? = Have you received any reply?
(This is the present perfect form of the verb ‘get’. It refers to time in the past up to now.)

[size=75]“Theirs is not to make reply: Theirs is not to reason why: Theirs is but to do and die.” ~ Alfred Lord Tennyson[/size]

Thanks Esl_Expert for such a nice explanation.

In addition, in standard British English the equivalent term would be more likely to be:
Have you had a reply?

Thanks Beeesneees.