iPhone not accepting IMAP password for email accounts

The IMAP password is how mail is received and existing mail read.

Here is what Apple suggests doing: If you can't receive email on your iPhone or iPad - Apple Support

Try logging into the webmail interface for the mail account.

Rilza wrote:

My iPhone keeps asking me for my iMAP password. I thought it was correct, but will not accept. I have several email accts.

Have you tried deleting the accounts and adding them back?