my HDMI cable does not fit the Apple TV HDMI input. What should I do?

Why not? What happens when you try exactly?

HDMI is a universal standard. All HDMI cables are the same size and shape, and all ports are the same size and shape to receive the cable. If your cable is not fitting into the port, then either the cable has an issue or its not an HDMI cable.

Easiest thing to do if your cable has a problem, or is not an HDMI cable, is to buy a new cable.

HDMI cable:

HDMI port on an Apple TV.

Incidentally it's longer side uppermost - the other way round from what's shown in the image - which is just a little counter-intuitive.

Yes, but neither the Apple TV nor any TVs I know about use those HDMI sizes. So unless you have a specific device that uses those, the reality is you won't actually come across them.

If you search for HDMI or ask for an HDMI cable in a store, its exceedingly unlikely you'll get one of the smaller sizes.

All HDMI cables are the same size and shape, and all ports are the same size and shape to receive the cable.

Then came Mini-C and Micro-D … 😉