That still doesn't make sense of the question.......

The question seems to be:
how do you add the -gi suffix to at (horse)
The problem with this is that there is no such thing as a -gi suffix and the -i suffix does not cause consonant mutation to form -ği when added to "at".

So the answer to the question seems to be:
atgı which is not a valid word formation!

And I read this just when I think I ahev sorted out how to greet people in Türkiye :-S

*wonders if she will ever get the hang of this language*