I am going to get a tattoo just like the majority of people on this site. I would like to get "Never Fear" in ancient greek.
Your request will soon be transferred to the appropriate thread: Tattoos and Ancient Greek (top of page).
Of course you can say this in modern Greek!
Mείνε ήσυχος is one obvious free translation,
Ποτέ μην φοβάσαι is a bit more literal. and I'm sure there are other options.
There were, and still are, many different dialects (not "types") of Greek, but in ancient times generally
μήποτε φοβοῦ (singular) or
μήποτε φοβεῖσθε (plural) would be understood by all to mean "Never fear." It's certainly valid for the Attic dialect of Greek, which is only considered "good" because so many great works of literature were produced by Athenians who grew up speaking it.