Unfortunately, getting a government seat for BSc Nursing in West Bengal with a JENPAS rank of 22270 SC is highly unlikely.
The cut-off ranks for government BSc Nursing colleges in West Bengal, especially for the SC category, are generally much lower. While you belong to the SC category, which offers some advantage, the competition is quite stiff.

Given your rank, you have a higher chance of securing a seat in a private nursing college in West Bengal. Many private colleges offer good quality education and placements. You can also explore nursing colleges in others states.

For more information about nursing colleges you can click the link attached below.

https://medicine.careers360.com/colleges/list-of-nursing-colleges-in-india