You must not believe such a story one bit.

Literal

Such story [topic-は] a-little-[even-も] believe-[prohibition-てはいけません].

少しも…てはいけません 'must not...even a little' — 少しも with a negative is emphatic: 'not even slightly.' ~てはいけません is the polite prohibition form. Firm and authoritative, like a warning or moral instruction.