problems with extension of my resident permit

I assume you have a family  reunion visa (FRV) , tied to the visa of your husband.

In that case, they should extend your permit until the vaidity of your husband's ends - because you two staying together is the point of a FRV. Did they actually refuse that, or did you apply for a longer extension?

They of course cannot extend a FRV beyond the sponsor's permit (here your husband). If you want that, you need to get permit on your own merit (e.g. by finding an eligible job).

@beppi

" assume you have a family  reunion visa (FRV) , tied to the visa of your husband.

In that case, they should extend your permit until the vaidity of your husband's ends - because you two staying together is the point of a FRV. Did they actually refuse that, or did you apply for a longer extension?

They of course cannot extend a FRV beyond the sponsor's permit (here your husband). If you want that, you need to get permit on your own merit (e.g. by finding an eligible job)."

My husband has Niederlassungserlaubnis. His permit finishes in 2028.

Mine is not Niederlassungserlaubnis. So I applied for an extension. They said they cannot extend. They need a new contract from my husband's job. He works on project basis at uni. His current project / contract finishes in November. So Ausländerbehörde tells me to bring a new contract from my husband. My husband is waiting for the results of the projects he has written. But the approve or an answer may delay, we may have to wait till 2024.

Hence, my questions and anxiety. what can I do right now and will they send me back to our home country while my husband stays here?

The situation does not become clearer by repeating what you wrote before.

I still think my assessment is correct, IF you have a FRV (which you neither confirmed nor denied).

But if your Ausländerbehörde sees it differently, they are either corect or you'd have to sue - a lengthy and costly option!