What is right: "get something back" or "get back something"?

For example:

• The service was very bad, so I want to get back a part of my money.
• The service was very bad, so I want to get a part of my money back.

What case is right and why?

Google Translator says the second variant is right. But it comes from the translation of a German phrase, in which the part "back" ("zurück") stays at the end of a sentence.

The Oxford Dictionary of Phrasal Verbs classes this usage of the transitive multi word verb get back (= 'recover [something] [one previously possessed]') as optionally separable, meaning that the orders

[simplex verb] [transitivising particle] [noun phrase] and

[simplex verb] [noun phrase] [transitivising particle]

will both be met with.

However, ODPV stresses in the preface that with such multi word verbs, it is far more idiomatic to postpose the particle with short NPs (indeed, it is ungrammatical not to do so with prepositions):

• If you lend him your gloves, you'll never get them back. [not get back them]
• Did you get your car back from the garage? [get back your car rather unusual]

And the reverse is true with weighty NPs:

• Did you get back that marvellous tool for extracting tacks and nails that you lent to Alice?

................

The NP 'a part of my money' falls in the middle lengthwise; you can confidently separate the MWV get back, or choose not to. Claims that only one variant is acceptable / normal are overprescriptive.

What you ask in your question's title is different from what you ask in its text, so I'll guess that the latter is what you really mean to ask.

One test you can apply is to use a pronoun for the object. "I want to get it back" is correct but "I want to get back it" is not. This shows that "get back" is one of those phrasal verbs where the idiomatic order is 1. verb (get) 2. object 3. particle (back).

English also allows the order 1. verb 2. particle 3. object if the object is sufficiently heavy (i.e. long or complicated). Whether this applies in any particular case is a matter of style and opinion. The single word "something " is not heavy enough. However, you might or might not think that the noun phrase "a part of my money" is indeed heavy enough to allow the wording "I want to get back a part of my money.". Despite what Kate Bunting.wrote, the words "of my money" are not superfluous and bear on the question of heaviness.

Get [something] back is the usual version (the 'ofs' in your heading are superfluous).

Your first version would be acceptable, but the second is much more idiomatic.