If you can log in your account in your browser, then the password is correct UNLESS you have setup two step authenticaition and it requires an app specific password.
To eliminate any issues on in Mac Mail, test in Guest User or create a new User to see if Mail works as expected.
CREATE A NEW USER
Go to System Preferences --> Create a New User in Users & Groups.
Switch to the New User by logging out under the Apple in the Menu Bar.
Log into the new User.
You can skip logging in with an Apple ID. Hit continue then skip.
Only Apple apps will be in the Dock.
Open Mail
Add your account.
If it works no need to let it download everything.
Note: if it's POP account be sure you set to "leave on server".
Quit Mail then log back into your regular User.
Open Mail
Remove the account. It will take you to System Preferences > Internet Accounts
Uncheck the account.
Go to your User's Library (see below)
Scroll down to Containers
Delete "com.apple.mail" folder
Log out under the Apple in the Menu bar
Log in
Open System Preferences > Internet Accounts and add account
Open Mail and see if it will connect.
There are other files that might need to be deleted, but let's try first with just Containers file.
Show User's Library
The User's Library folder is hidden by default. To unhide: Select the Finder in the Dock. Under Go in the Menu bar > hold down the Option key and you’ll see the Library.
Finding the User Library Folder
http://www.takecontrolbooks.com/resources/0167/site/chap11.html#FindingtheUserLi braryFolder