1.Some boy or other has stolen by book.

here "other" is functionin as "pronoun" or "noun"?

or "other" means "other boy".

Should I write it like

Some boy or other boy has stolen my book.

Then here "other" works as "adjective"

Please clear my doubt.

An interesting case, Hanuman. I have heard this expression, 'some guy or other has stolen my gal' for instance. Looking at it, however, I cannot help but think that it is incorrect in any formal usage, which would more properly be 'some/one boy or another', where of course 'another' is an adjective serving as a pronoun (replacing 'another boy').

The indefinite form is 'some/one boy or another', while the definite form would be 'one boy or the other' (where there are only two boys under consideration).