What is the proper apostrophe placement for using the letter N in place of the word "and"?
In reality, you may mostly find the shortened form of and written as 'n, -- one apostrophe before n.
The rationale can be found in its evolution. In informal use, words ending in ing started appearing with the final g dropped: goin'. This has extended to many words with a penultimate n, so and became an'.
Next shortening, confined almost exclusively to the word and, dropped the a -- when it was written variously as 'n' / 'n.
Even now both the forms can be seen.
Since you are replacing letters before and after, 'n' is the most common. I don't know that there is a "proper" placement though.
In some sense, since replacing the "and" with "n" is not standard, there'll be no actual standard for the spelling either. But if a standard is really 'anything that doesn't look too weird, then you'd write it with an apostrophe for everything eliminated (that's the normal operation of an apostrophe), that is, an apostrophe on either side of the "n":
cheese and rice
cheese 'n' rice
Alternatives that work and are used
cheese 'n rice
cheese n' rice
the latter being the most common.