The $q$-Whittaker functions, which are $t=0$ specializations of the Macdonald polynomials $P_\lambda(X;q,t)$ are known to expand positively as the sum of Schur polynomials, which are $q=t=0$ specialization of the Macdonald polynomials. Macdonald polynomials have a quasisymmetric refinement; quasisymmetric Macdonald polynomials $G_\gamma(X;q,t)$ and a nonsymmetric refinement; the ASEP polynomials $f_\alpha(X;q,t)$. We study the $t=0$ specializations of both these polynomials and show that at $t=0$, the ASEP polynomials expand positively as a sum of Demazure atoms, $\cA_\alpha(X) = f_\alpha(X;0,0)$, which are the nonsymmetric refinement of Schur polynomials. Using this we will show a similar result in the quasisymmetric setting, i.e., we show that $G_\gamma(X;q,0)$ expands positively as a sum of quasi Schur polynomials $\QS_\gamma(X) = G_\gamma(X;0,0)$, which are the quasisymmetric refinement of the Schur functions. We also give the description of the coefficients in both the cases in terms of the charge statistic on tableaux.