How to export a seamless pattern in different sizes without having to match the sides

Try the pattern maker (Object > Pattern > Make) to define the size of your repeating tile.

Be careful with metric measurements if you want to export as an image, use pixels instead.

Illustrator can automatically convert between units, so if you document is setup in pixels or points you can type 3cm in a width or height box and it gets converted to pixels.

3 cm = 85,0394 px which shows the problem.

An fractional 0,0394 pixel does not exist so you should use 85 px instead (which is 2,9986 cm).

This to avoid additional unwanted pixels.

If you do not export your patterns as images or design for screens, ignore this.