If there is an Eastern eparchy (diocese) which covers that territory for that particular Eastern Church sui iuris then each bishop would have jurisdiction over his own parishes and parishioners. There is no “shared jurisdiction.”
However, it sometimes does happen–not so much at the present, but certainly in the past, that there is an Eastern parish which has no bishop of its own. In that case, the local Latin bishop is the bishop of that Eastern parish. Depending on when certain eparchies (or exarchies) for Eastern Catholics were established, we go back just a few years, or many decades. I cannot name any offhand, but there may be a few isolated Eastern parishes still in the US. Actually, there “probably” are, I just cannot name any.
Just for example, the Syrian Catholic Eparchy of Our Lady of Deliverance was not established until 1995. Before then, the Syrian parishes were under the jurisdiction of the local Latin bishops.
So yes, it is possible to have a Latin diocese that happens to have an Eastern parish as part of that diocese.