Ryll-Nardzewski theorems states that if $T$ is a countable complete theory, then $T$ is $\aleph_0$-categorical if and only if for every $n<\omega$ there are only finitely many formulas $\varphi(x_1,\ldots,x_n)$ up to equivalence relative to $T$.

$T$ is a countable theory if it can be built in a countable language.

My question is: Is there a complete uncountable theory which is $\aleph_0$-categorical, but that for some $n<\omega$ there are infinitely many formulas $\varphi(x_1,\ldots,x_n)$ up to equivalence relative to $T$?

Thanks