أَيُّ = which خِدْمَة = service (can mean "favor" as well) so the Lit. translation will be = which service ? And have you noticed the word خِدْمَةٍ ends with a Ta Marbuta ـة with double Kasra, that means that the noun is indefinite, and most important, the noun is in the genetive case (الجَرّ)

It is a specific term of hospitality and culture, generally asked by Arabs. أي خدمة ؟ means Any help? The detailed meaning is لو تامرني باي خدمة انا مستعد للعمل بها "If you ask me for any help, I am ready to do it. In view of grammar, it is in the place of جار و مجرور جار or preposition is here understood.