  In this note, we study the twisted Jacquet modules of sub-quotients of
principal series representations of ${\rm GL}_2(D)$ where $D$ is a division
algebra over a non-archimedean local field $F$. We begin with a proof of a
conjecture due to D. Prasad on twisted Jacquet modules of Speh representations
of ${\rm GL}_2(D)$ when $D$ is the quaternionic division algebra. Later, when
$D$ is an arbitrary division algebra over $F$, we focus on depth-zero principal
series and compute the dimensions of twisted Jacquet modules of generalised
Speh representations and investigate their structure explicitly.
