Does Minato still have Yin-Kurama? I thought Minato kept Yin-Kurama because I heard that Minato gave Naruto most of his nine tails chakra, but not all of it.

I wonder if Minato still has some of the Yin-half Kurama. If not please explain it to me.
I don't believe he does.

During the final battle, Madara largely succeeded in his goal of extracting Kurama out of Naruto.  This meant that Naruto was going to die if something weren't done.

Enter Minato and Yin Kurama.  A transfer of Yin Kurama was made into Naruto from Minato so that he would survive having Yang Kurama extracted from him.

It isn't the case that Minato contains Kurama any longer.