The local bishop of the place has jurisdiction over all priests in his diocese save those incardinated into other overlapping ordinaries’ jurisdictions (ordinariates, ECC’s Eparchies, personal prelatures, religious orders).
Within most of the west, the local territorial ordinary is the Roman Rite bishop.
Where overlapping juridictions exist, people are under the care of their own bishop or ordinary if his jurisdiction overlaps, or under the care of the local Roman if not.
In the continental US, if you’re Ruthenian, Ukrainian, Slovenian, Italo-Albanian, Chaldean, Syro-Malabar, Syro-Malankar, Maronite, Melkite, Romanian, you have a bishop (The Slovenians and Italo-albanians are assiged to the Ruthenians by Rome; if you’re Anglican in Union with Rome, you’ve a non-bishop as your Ordinary, but he has the same authority (just can’t ordain people).
In the Continental US, if you’re Russian GCC, you’re under your local roman bishop.
The others, I’m not certain.
Religious gets complicated - but generally, Religious priests assigned to a house of their order are not under the local bishop; Religious priests on loan to a diocese come under the authority of the bishop (but they generally aren’t supposed to be doing that anymore). Within the walls and/or grounds of a religious community’s house/priory/convent/monastery/abbey of the western church, you’re outside the authority of the bishop. Eastern Monastic Communities are traditionally under the authority of a particular bishop - usually either the local bishop or the patriarch, but some are papal right and thus almost exactly like the western orders for this purpose.
