Does (did) German have something like what they call possessive apostrophe
If not, what does the role of it in German language?
This is my father's hat.
My best friend's husband.
German attaches the genitive suffix without an apostrophe.
Das ist meines Vaters Hut / Das ist der Hut meines Vaters
Der Mann meiner besten Freundin
Julias Mann. Martins Frau.
You will occasionally see " 's " as a genitive ending in German,
but that is - to put it mildly - inspired by English orthography, and incorrect in German.
No, it doesn't. German has a possessive -s without the apostrophe.
Das ist der Hut meines Vaters.
Der Mann meines besten Freunds.
Using a possessive apostrophe anyway is a fairly common mistake, especially by people whose native language is English, but it's certainly not correct.
Your question has already been answered very well. But to add some more information about the meaning of German apostrophe: In German, an apostrophe is always the hint that one letter is missing (in direct speech also more than one letters) even though many people use it in the wrong sense.
Wie geht es: Wie geht’s
Explanation: The letter ‘e’ of es is missing
Der Computer gehört Franz/Max/Hans/Maurice (last "spoken" letter is an s):
Es ist Franz’/Max’/Hans’/Maurice’ Computer.
Explanation: Genitive 's' at the end of the names Franz/Max/Hans/Maurice cannot be pronounced and is therefore replaced with an apostrophe. Which is indeed an apostrophe at the end of a genitive word. But it has nothing to do with the genitive. It’s just because one letter is missing.
No, in general the German language does not have an apostrophe in that case.
Im Gegensatz zum Englischen wird der deutsche Genitiv ohne Apostroph geschrieben. DeutscheGrammatik20
Englisch: Peter’s house
Deutsch: Peters Haus
There's one exception to the rule. If the name already ends in an -s, an apostrophe is used to indicate the genitive. It's better to reword it, not least because once you read it aloud you lose that indicator.
Einen Apostroph bekommt der Genitiv im Deutschen nur, wenn der Namen bereits auf –s endet. Hier sollte der Genitiv aber besser durch die Präposition von ersetzt werden.
Genitiv mit Apostroph: Klaus‘ Haus
besser: das Haus von Klaus
There are certain other webpages that summarize that topic. Another trustworthy site is Lingolía. They recognize a second exception:
Eine weitere Ausnahme besteht, wenn die Grundform von Namen besonders herausgestellt werden soll. Dann ist auch folgende Schreibung erlaubt. Lingolia
Beispiel: Andrea’s Armbrust
An apostrophe can make an important difference between male Andreas and female Andrea. Example:
Andreas' Bruder wohnt in Andrea's Haus.
In oral language, there's no distinction whatsoever; but in written language, the apostrophe makes the difference.
There is no such thing as the genitive apostrophe known in English (*). In German, the genitive "s" is attached without an apostrophe:
Der Hut meines Vaters
Andreas Friseursalon (it belongs to Andrea)
Only if the noun already ends with a spoken "s"-sound, an apostrophe is appended to avoid ambiguity:
Andreas' Friseursalon (it belongs to Andreas)
(*) The so called "Deppenapostroph" (idiots' apostrophe) exists, mostly to make fun of people who use the English form in German, or even worse things like the famous Weihnacht'smann or Kartoffel'n.
I guess the answer is yes, the English apostrophe is sometimes adopted. I came to this conclusion after noticing that my favorite grocery store where I was staying in Königswinter is called “Kaiser's”.