Kindly provide e-mail documentation between you and customer.
Kindly provide an e-mail documentation between you and customer.
which one is correct.
***Neither a teacher nor a native-speaker***
Apart from articles, e-mail documantation doesn't make sense to me. If you mean providing documents by documentation then it should be ...documentation via/by/through. But if you mean documents (plural) by documentation then it should be ...documentation sent via/by/through.
In a nutshell, I don't think that an e-mail itself is a document. But I can't say for sure what might be the process for, let's say, the courts to regard e-mails as documents.