From definition of $o$ and $\omega$
one states that $0 < c_1\cdot g(n) < f(n)$ for $n > n_0$ and some $c_1$ and another states that $0 < f(n) < c_2\cdot g(n)$ for $n > n_1$ and some $c_2$
It seems like there is no such function that satisfies condition. But i can't show this rigorously.