Not any that were mentioned

The half breeding was discouraged during those times and Ministry had put many rules regarding it, so therefore there weren't any half breeds

Any reason why?

I'd really like to know the reason for laws like that.

^ Everybody knows ministry hates Non Wizarding kind until after the second war...And I am damn sure they would have implemented these laws(with people like Umbridge) to harass these creatures...So ig this is the reason they would have created this laws

Now I’m wondering if there were any half-breeds who worked in the ministry

^^Bloody good Reason to change them now.

^ you bet there aren't. It's a bit like LGBTIQ* - no lobby no support.

I think they were very rare even before the laws. I mean first of all it has to be physically possible (I have no idea how a giantress and a human... nevermind) they have to be compatible ("cross breeding" is often impossible in the real world. Genetics are too different which is why you could e.g. not mate a horse with a monkey but a horse with a donkey even though the offspring often is infertile at best) so the species have to be close enough to allow fertilisation and birthing.

Then there's the social stigma, you can bet it's not socially accepted to have a partner from another species.

Rare indeed.

Allow me to add an on topic fanfiction meme from another fandom: dwarf X elf

Technically there was Fleur, who was part Veela (though not half, and although she wasn't a student at Hogwarts, she was a student that went to Hogwarts at some point)