Capitalise the initial "a", apostrophise the word "mines", add a full stop (or delete the existing one) to "t.v" and capitalise it. A friends of mine's father is a TV (or T.V.) repairman.
It is grammatically correct, but it is a bit clumsy and potentially confusing because mine is already possessive.
Pfft a perfectly cromulous usage here... Please Register or Log in to view the hidden image! Actually I have used it myself on numerous occasions.
It's acceptable in speech. You're very unlikely to encounter that construction in writing, except as colloquial dialog within quotation marks. When writing, people will usually either: Shorten it to "my friend's father" or "a friend's father," or... Straighten out the grammar to "the father of a friend of mine" or "the father of one of my friends." It was a reasonable hypothesis since your punctuation here is pretty sloppy, for example, your consistent failure to capitalize the pronoun "I" and the first word in your sentences. Punctuation errors slow the reader down. Not taking the little bit of time you need to learn the location of your Shift key by touch multiplies the impact by causing everyone who reads your writing to waste their own time. In other words, it's rude.
Regardless, when you post the comment "Fix my sentence" without specifying which errors you're aware of and which you aren't it leaves the whole thing open to to scrutiny and correction. And the comment "i know about the punctuation" was also particularly ingenuous, since most of the corrections, including the looked-for one, was punctuation.