I just cannot see the Turkish tree but I guess you haven't learned the 'ki'-lesson up to now. So you might see it later on.
In the sentence in question the 'ki' ending changes a personal pronoun into a noun.
my -> mine
benim -> benimki
You could say ""ben senin şahidinim." This is just an alternative, yet equally valid way to word that. The ending on "ben" might be throwing you off. It looks like "benim" as in "my," bu it is actually "ben + -(y)Im" which is "I + 1st person singular copula (like am)"