To update Email, mobile in BSE go to Invest Online BSE >> Profile list menu in Investwell Mint. Here, go to Edit UCC from the actions on the right.
You can change the Email, mobile no. and click on the Submit button at the bottom of the page.
Relevant links
To update Email in Kfintech
https://mfs.kfintech.com/investor/Transact/ChangeFolioEmail