right click the account in the folder pane and select the cox folder you want to use in the subscribe list

Goto account settings > Junk Settings and specify the folder to be used for junk mail by Thunderbird.

Normally the server identifies the spam/junk folder when Thunderbird checks the server capabilities and folders and Thunderbird uses it, so I guess cox missed that part of their server configuration.

Thank you for your suggestions. I subscribed and refreshed all the email accounts. It seems I have to set TB to Other>Junk on that email and that seems to create in the TB listing of Junk two folders-one for Junk and one for Spam. Neither seems to show in the count of Junk on TB but I do see them. What is frustrating is on an iPhone, Cox email labels the main Spam folder as Junk on the iPhone and on its webmail it is labeled as Spam so If I send to Junk on iPhone it really goes into Spam and if I am on webmail and mark it as Spam (no option for Junk) it too goes into Spam so I need to see that Spam folder in TB. Seeing both folders spam/junk in the TB Junk listing kind of resolves that. (very confusing and frustrating to have to think all the options). My issue now remaining is on TB, when I mark a message as Junk (clicking the little flame icon next to the email), it puts it automatically into the Junk folder just fine but also MARKS IT AS READ! How do I stop TB from marking a Jun email as read automatically?

Menu app icon > 'Preferences' > 'Privacy & Security' Scroll down to 'Junk' section. Uncheck checkbox 'Mark messages determined to be Junk as Read' So it is not selected.

It is unchecked so I checked rebooted and again unchecked and alas it still marks as read when I mark an email Junk in the inbox.