  In Geometric function theory, occasionally attempts have been made to solve a
particular problem for the Ma-Minda classes, $\mathcal{S}^*(\psi)$ and
$\mathcal{C}(\psi)$ of univalent starlike and convex functions, respectively.
Recently, a popular radius problem generally known as Bohr's phenomenon has
been studied in various settings, however little is known about Rogosinski
radius. In this article, for a fixed $f\in \mathcal{S}^*(\psi)$ or
$\mathcal{C}(\psi),$ the class of analytic subordinants $S_{f}(\psi):= \{g :
g\prec f \} $ is studied for the Bohr-Rogosinski phenomenon in a general
setting. It's applications to the classes $\mathcal{S}^*(\psi)$ and
$\mathcal{C}(\psi)$ are also shown.
