פירוש על שבת 43:2

It is a commandment to place it in the courtyard or the public domain a handbreadth away from the entrance. As if he moves it further from the entrance, it will not be noticeable that the head of the household put it there.

On the right: When he enters his house, it is to the right.

Mezuzah: It is established for us, that it is on the right. For it is written, "your house" (beitekha) - [and expounded to mean,] the way you arrive (biatekha); and when a person raises his foot, he raises his right foot first.