I'm pretty new to Photoshop. I would like to change the color of this object on my .png image:
But anyway I try, it becomes this fuzzy with the new color:
How can I change it's color to stay in it's original shape?
There's multiple ways. The easiest would be to add a 'colour overlay' layer style.
This is a non-destructive effect (you can revert or alter it as needed), but only if you save it as a *.psd file. If you save as *.png, it will just be the new colour.
A more direct way might be to destructively alter the pixels' colour:
Since it's the loss of opacity anti-aliasing that creates your unwanted effect, locking the opacity will prevent this from happening.
EDIT: As proposed by Larme in their comment, here is another non-destructive method:
This way, the bottom layer's transparency act as a mask for the top layer.
Find the 'Lock Transparent Pixels' button
Then fill everything with the colour you want.