  The aim of this article is to give a characterization of strongly
quasipositive quasi-alternating links and detect new classes of strongly
quasipositive Montesinos links and non-strongly quasipositive Montesinos links.
In this direction, we show that, if $L$ is an oriented quasi-alternating link
with a quasi-alternating crossing $c$ such that $L_0$ is alternating (where
$L_0$ has the induced orientation), then $L$ is definite if and only if it is
strongly quasipositive (up to mirroring). We also show that if $L$ is an
oriented quasi-alternating link with a quasi-alternating crossing $c$ such that
$L_0$ is fibred or more generally has a unique minimal genus Seifert surface
(where $L_0$ has the induced orientation), then $L$ is definite if and only if
it is strongly quasipositive (up to mirroring).
