We consider an $n-$dimensional locally product space with $p$ and $q$ dimensional components $(p+q=n)$. In our previous paper, we have considered two connections, $(F,g)-$holomorphically semi-symmetric (this means that both metric and structure tensor are parallel towards this connection) and $F-$holomorphically semi-symmetric one, both with gradient generators. We have proved that both of these connections have curvature-like invariants which are both equal to product conformal curvature tensor. Here we shall consider the third connection from this family, namely, $g$-holomorphically semi-symmetric connection and find its curvature-like invariant.