In Jain Dharma, the next cycle means the coming Utsarpiṇī kāla after the present Avasarpiṇī kāla.

For that future cycle:

• There will again be 24 Tirthankars.
• Their complete life stories are not popularly detailed in the same way as the present Tirthankars of this cycle.
• Jain scriptures mainly describe the general pattern:

1. They are born in noble royal families. 2. They live in purity and detachment. 3. They renounce worldly life. 4. They attain kevaljñān. 5. They establish the fourfold Jain Sangh and the path of liberation.

So, in short, the “stories of the 24 Tirthankars of the next cycle” are understood in Jain tradition as future divine events, but their detailed biographies are not commonly given in the same narrative form as the current cycle’s Tirthankars.

If you want, I can also give:

• the names of the future 24 Tirthankars according to Jain tradition, or
• a simple explanation of Utsarpiṇī and Avasarpiṇī.