sorry to bother you, but I got another question. I appreciate all your comments. Thanks a lot.
Let $\mathfrak{A}$ be countable and ${\aleph}_0$-categorical. If $X \subset |\mathfrak{A}|^n$ is invariant under automorphisms of $\mathfrak{A}$ then $X$ is definable.
I assume that by definable you mean $\emptyset$-definable.
So the hint is: prove the fact that whenever you have a set $X$ definable over some small set $B$ in a saturated model $M$, and such that for some other set $A$ we have that any automorphism fixing $A$ fixes $X$, then $X$ is definable over $A$. What you're trying to prove will follow (since if a theory is $\aleph_0$-categorical, then the countable model is saturated).