What is the minimum time that a soul that has incarnated in one of the seven levels of Naraka in Jainism will stay there?
Minimum time: 10,000 years. In the first Naraka (the lowest hell), a soul stays at least ten thousand years; in the other Narakas the stay is longer, up to extremely long periods measured as sagaropama (for the seventh Naraka the maximum is 33 sagaropama years). These are the fixed lifespans of hellish beings in Jain cosmology and apply to Naraki beings, not to humans. The overall scheme is described in canonical Jain texts and is accepted by both major Jain traditions.
You can read more here and about how the time units like attam relate to lifespan in Naraka .