The footage pretty much shows the problem:

When I move text slower than a pixel at a time, it doesn't move in subpixels, instead it jumps from pixel to pixel. How can I fix that?
I searched for days, still nothing that could help me with that.
Let me know if I need to show code of some part, I can upload everything, but it'll be a lot to fit in here.

Thanks for the help in advance, hope it will resolve.