The translation of the preposition 'außerhalb' into English is given as:
(area) 'beyond', or 'outside of'
(period of time) 'outside'
The distinction, if any, between 'outside' and 'outside of' is not well defined. Similarly 'inside (of)'. Both usages are commonly encountered, with area, time or other quantities. Strictly the 'of' is superfluous, at least in British English, where it is sometimes regarded as being rather colloquial.
(Although there may be a vague quality of possession around the words 'inside' and 'outside', they do not require a possessive in English, unlike their German equivalents, e.g. ‘innerhalb / außerhalb des Hauses’.)
However, there is another English word, which I invite you to show as a translation of 'außerhalb'. It is 'outwith', a word that may date from the 13th century. Although it may be said to be a regional dialect word largely confined to the far north of England and to Scotland, it is also heard from time to time on the BBC, and possibly with increasing frequency. It is a very useful word that a) circumvents the question of 'outside / outside of', and b) allows very compact constructions whether the subject is area, time or anything else.
I) The lady sought the view of an expert outwith her local health authority.
II) The normal range of body temperature is 36.5–37.5 °C; outwith this range, a patient may present symptoms of ill-health.
This is my first posting on 'WordReference'. I look forward to hearing the views of others.