Look at the picture.

A table is in the middle.

1. A chair is on the right.
2. A chair is at the right.

3. A chir is on the right of the table.
4. A cahir is at the right of the table.

(Which preposition do we have to sue? Which ones are grammatical?)

"on" is the better of these two prepositions to use in these sentences. "at" is not incorrect, but "on" is simply smoother.