Senaa7
I hope I got you right, as the wording of all that stuff isn't always too easy to understand:
(a page is not the same as a site, and so on)
You have created a "Team Site" and a "Communication Site"? (Those are the 2 default options when you start to create a site based on the modern experience - see details below)
Then you want to use the SharePoint News Connector in Teams to show "News" from the communication site, correct?
It's not possible to use the News Connector with another site than the group-associated "Team Site" from my knowledge.
What you can do however is, to add a tab to your Team Channel and display the Communication Site Start Page (including the News Webpart) for example.
But if you want to work in a Team, why would you need another scope for news in an extra site?
Details:
a Team site covers "Collaboration" scopes and is bound to a O365 Group - the same group that you are using in Teams
--> this one is for "we are a Team and everyone in this Team works here equally on the content" - per default every Member of the Team has the permission to edit the content
a communication site covers "Publishing" scopes and is not bound to an O365 Group
--> This one is more like "only some people add and edit content and many others just consume it"
per default no permission is set here, you would need to define who will be editing the content and who will just view it